Quadratische Funktionen/Kapitel 5: Die Scheitelpunkts- und Normalform und der Parameter a und Use of English/Word Families/Overview: Unterschied zwischen den Seiten

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{{Box|1=Die Scheitelpunkts- und Normalform und der Parameter a|2=


'''In diesem Lernpfad werden alle erlernten Parameter zusammengeführt! Bearbeite den unten aufgeführten Lernpfad!'''
Word from the same '''word families''' can be easily understood because they share a common root and pre- and suffixes you can identify.


*Die Scheitelpunktsform und der Parameter a
Words in '''bold''' are commmon and important to learn.
*Aufgaben zu "f(x) <math>=</math> a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>"
*Die Normalform und der Parameter a
*Vermischte Aufgaben zur quadratischen Funktion
|3=Lernpfad}}


{{Navigation verstecken|{{Vorlage:Quadratische Funktion}}}}
== A ==


Aus den vorherigen Lerneinheiten kennst du die Eigenschaften der einzelnen Parameter.
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| ability, disability, inability || enable,disable|| '''able''', unable, disabled || ably
|-
| acceptance || '''accept''' || acceptable, unacceptable, accepted ||-ably
|-
| '''accident''' ||  || accidental || -ally
|-
| accuracy, inaccuracy ||  || '''accurate''', inaccurate || -ely
|-
| accusation, the accused, accuser || accuse || accusing ||
|-
|achievement, achiever || '''achieve''' || achievable ||
|-
|act, '''action''', inaction, interaction,<br>reaction, transaction<br>actor, actress ||  '''act''' || acting ||
|-
|activity, inactivity || ||'''active''', inactive, interactive, proactive activate || actively
|-
|addition || '''add''' || additional || additionally
|-
|admiration, admirer || '''admire''' || admirable || admirably
|-
|'''advantage''', disadvantage || ||advantageous, disadvantaged || advantageously
|-
|'''ad'''(vertisement), advertiser,|| '''advertise''' || advertising ||
|-
|'''advi<span style="color:red">c</span>e''', adviser|| '''advi<span style="color:red">s</span>e''' || advisable,inadvisable, advisory ||
|-
|agreement, disagreement ||  agree, disagree || agreeable || agreeably
|-
|aim || to aim || aimless || aimlessly
|-
|amazement || amaze || amazed, amazing || amazingly
|-
|anger<br>(anger management) ||  anger || angry || angr<span style="color:red">i</span>ly
|-
|announcement, announcer || announce || unannounced ||
|-
|appearance, disappearance<br>reappearance || appear, disappear, reappear ||
|-
|applicant, application || apply || applicable,applied
|-
|appreciation || appreciate || appreciable,appreciative ||
|-
|apprentice, apprenticeship ||  || ||
|-
|approval, disapproval || approve, disapprove || approving, disapproving ||  approvingly
|-
|approximation || approximate || approximate || approximately
|-
|argument || argu<span style="color:red">e</span>  || arguable, argumentative || arguably
|-
|arrangement || arrange, rearrange ||
|-
|art, artist, artistry || || artistic, artful || artistically
|-
|shame || shame || ashamed, unashamed, shameful,shameless ||  shamefully, shamelessly
|-
| attachment || attach, detach || attached, unattached, detachable, detached<br> (semi-detached house) ||
|-
|attack, counter-attack, attacker || attack, counter-attack || ||
|-
|attention || attend ||attentive,inattentive || attentively
|-
|attraction, attractiveness || attract || attractive, unattractive || attractively
|-
|authority, authorization || authorize || authoritarian, authoritative, unauthorized ||
|-
|availability || || available, unavailable
|-
|avoidance || avoid || avoidable, unavoidable ||
|-
|awareness || || aware, unaware ||
|}


Du weißt zum einen, dass der Vorfaktor a für eine Streckung, Stauchung und Spiegelung der Parabel verantwortlich ist und zum anderen, dass die Parameter y<sub>s</sub> und x<sub>s</sub> eine Verschiebung der Parabel in der Ebene bewirken.
== B ==
Wir wollen im Folgenden diese Eigenschaften zusammen mit der Scheitelpunkts- und Normalform betrachten.


Als erstes beginnen wir mit der Scheitelpunktsform und dem Parameter a.
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| base,the basics,basis || base (on) || baseless, basic || basically
|-
| bearer || bear || bearable, unbearable ||
|-
| beat, wife-beater || beater || beating unbeatable,unbeaten ||
|-
| beauty, beautician || to beautify || beautiful || beautifully
|-
| beginner, beginning || begin || ||
|-
| behaviour/behavior ([[Amerikanisches Englisch|AmE]])<br>misbehaviour || behave, misbehave || behavioural/behavioral
|-
| belie<span style="color:red">f</span>, disbelief || belie<span style="color:red">ve</span>, disbelieve || believable, unbelievable || unbelievably
|-
| block, blockage || block, unblock || blocked, unblocked ||
|-
| blood, bleeding || bleed || bloodless,bloody ||
|-
| the boil, boiler || boil || boiling ||
|-
| bore,boredom || bore || bored, boring || boringly
|-
| break, outbreak, breakage || break ||unbreakable, broken, unbroken ||
|-
| breath, breather, breathing || breath<span style="color:red">e</span> ||breathless || breathlessly
|-
| brother, brotherhood || || || brotherly
|-
| build, builder, building || build, rebuild || ||
|-
| burn, burner || burn || burning, burnt ||
|-
| burial || bury || buried ||
|}


== C ==


==STATION 1: Die Scheitelpunktsform und der Parameter a==
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| calculation, calculator || calculate || incalculable,calculated, calculating ||
|-
| calm, calmness || calm || calm || calmly
|-
| capability || || capable, incapable || capably
|-
| care, carer || care for, about || careful, careless,caring, uncaring || carefully, carelessly
|-
| celebration, celebrity || celebrate || celebrated, celebratory ||
|-
| centre/center ([[Amerikanisches Englisch|AmE]])<br> centralization, decentralization  || center, centralize,<br>decentralize || central, centralized  || centrally
|-
| certainty, uncertainty || || certain, uncertain  ||certainly, uncertainly
|-
| challenge, challenger || challenge ||challenging
|-
| change || change || changeable,interchangeable, unchanged, changing ||
|-
| character, characteristic, characterization || characterize || characteristic, uncharacteristic || characteristically
|-
| chemical, chemist, chemistry || || chemical || chemically
|-
|circle, semicircle, circulation || circle, circulate || circular ||
|-
|cleaner, cleaning, cleanliness || clean || clean, unclean || cleanly
|-
|clarity, clearance, clearing || clear || clear, unclear  ||clearly
|-
|close,closure || close (schließen), enclose || (en)closed, closing
|-
| closeness || close (sich nähern)||close (by) || closely
|-
| clothes, clothing || clothe ||clothed, unclothed ||
|-
|collection, collector || collect || collected, collective || collectively
|-
|colour/color ([[Amerikanisches Englisch|AmE]])<br>colouring/coloring ||  color coloured, discoloured, colourless/colourful || colorfully
|-
| combination || combine || combined
|-
| comfort, discomfort || comfort || (un)comfortable, comforting  | comfortably
|-
| commitment || commit to || noncommittal, committed ||
|-
| communication, communicator || communicate || communicative,uncommunicative ||
|-
| comparison|| compare || comparable,incomparable, comparative ||  comparatively
|-
| competition, competitor || compet<span style="color:red">e</span> ||competitive, uncompetitive || competitively
|-
| complain<span style="color:red">t</span> || to complain (about) || ||
|-
| completion, incompleteness || complete || complete, incomplete || completely, incompletely
|-
| complication ||  complicate ||complicated, uncomplicated ||
|-
| computer, computing,<br> computerization || computerize
|-
| concentration || concentrate || concentrated ||
|-
| concern || concern || concerned, unconcerned
|-
| conclusion || conclude ||concluding, conclusive, inconclusive || conclusively
|-
| condition, precondition,<br>conditioner, conditioning  || condition || conditional, unconditional || conditionally,unconditionally
|-
| confidence || confide || confident,confidential || confidently, confidentially
|-
| confirmation || confirm || confirmed, unconfirmed
|-
| confusion || confuse || confused, confusing || confusingly
|-
| connection || connect, reconnect, disconnect || connected, disconnected, unconnected ||
|-
| consciousness,unconsciousness|| || subconscious,unconscious, conscious ||  consciously, unconsciously
|-
|consequence || || consequent, inconsequential || consequently
|-
|consideration || consider, reconsider || considerable,considerate,<br>inconsiderate,considered || considerably,  considerately
|-
| continent || || continental, intercontinental ||
|-
| continuation, continuity || continue, discontinue || continual, continued, continuous || continually, continuously
|-
| contribution, contributor || contribute || contributory
|-
| control, controller || control  || controlling, uncontrollable || uncontrollably
|-
| convenience,inconvenience || inconvenience || convenient, inconvenient || conveniently
|-
| conviction || convince || convinced, convincing, unconvincing || convincingly
|-
| cook, cooker, cookery, cooking || cook || cooked,uncooked ||
|-
| cool, coolness || cool down || cool || coolly
|-
| correction, correctness || correct || correct, incorrect,corrective || correctly, incorrectly
|-
| count, recount || count, recount || countable, uncountable, countless ||
|-
| '''courage''', encouragement, discouragement || '''encourage''', discourage || courageous, encouraged, encouraging, discouraging || encouragingly
|-
| cover, coverage, coverall || cover, uncover || covering undercover, uncovered ||
|-
| creation, creativity, creator || create, recreate || creative,uncreative || creatively
|-
| crime, criminal, criminologist || || criminal, incriminating incriminate || criminally
|-
| critic, criticism || criticize || critical, uncritical || critically
|-
| crowd, overcrowding || crowd || crowded, overcrowded ||
|-
| cruelty || || cruel || cruelly
|-
| cry, outcry || cry || crying ||
|-
| culture, subculture || || cultural, cultured || culturally
|-
| cure || cure || cured, incurable ||
|-
| custom, customer, customs || accustom, customize || customary || customarily
|-
| cut, cutting || cut, undercut || cutting
|}


{{Box|1=Quadratische Funktion "f(x)<math>=</math>a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>"|2=
== D ==


* Versuche mit Hilfe des "GeoGebra-Applets" den Lückentext zu lösen
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| damage, damages || damage || damaging, undamaged ||
|-
| danger || endanger || endangered, dangerous ||  dangerously
|-
| dare,daring || dare || daring || daringly
|-
| dark, darkness || darken || dark, darkened, darkening || darkly
|-
| date || date, predate || dated, outdated ||
|-
| day,midday || || daily || daily
|-
| dead, death || die, deaden || dead,  || deadly, deathly 
|-
| deal, dealer, dealings || dealt || dealt ||
|-
| deceit, deceiver, deception || deceive || deceitful, deceptive ||deceptively
|-
| decision, indecision || decide on || decided, undecided, decisive,indecisive || decidedly, decisively,indecisively
|-
| decoration, decorator || decorate || decorative || decoratively
|-
| deep,depth || deepen || deep, deepening || deeply
|-
| defeat, defeatism, defeatist || defeat || undefeated, ||
|-
| defence/ defense ([[Amerikanisches Englisch|AmE]]),<br>defendant, defender || defend || defenceless, indefensible, defensive ||  defensively
|-
| definition || define || definite, indefinite || definitely,indefinitely
|-
| demand, demands || demand || demanding, undemanding ||
|-
| democracy, democrat || || democratic, undemocratic || democratically
|-
| demonstration, demonstrator || demonstrate || demonstrable,demonstrative || demonstrably
|-
| denial || deny || undeniable || undeniably
|-
| dependant, dependence, independence, dependency  || depend on || dependable, dependent, independent  || dependably, independently
|-
| descri<span style="color:red">p</span>tion || descri<span style="color:red">be</span> ||describable, indescribable, nondescript, descriptive ||  descriptively
|-
| desire || desire || desirable, undesirable, desired, undesired
|-
| destroyer, destruction || destroy || indestructible, destructive || destructively
|-
| determination, determiner || determine || determined, predetermined, indeterminate|| determinedly
|-
| developer, development, redevelopment || develop, redevelop || developed, undeveloped, developing ||
|-
| difference, indifference, || differ from, differentiate  ||different, indifferent  || differently
|-
| directness,direction, <br>(to give) directions, director|| direct, redirect || direct, indirect || directly, indirectly
|-
| disagreement || disagree<br>(see also agree) || disagreeable || disagreeably
|-
| disappointment || disappoint || disappointed, disappointing ||  disappointingly
|-
| '''d<span style="color:red">i</span>saster''' || || disastrous || disastrously
|-
| disciplinarian, discipline || discipline || disciplinary, disciplined, undisciplined ||
|-
| discoverer, '''discovery''' || '''discover''' || ||
|-
| distance || distance || distant || distantly
|-
| disturbance || disturb || disturbed, undisturbed, disturbing || disturbingly
|-
| divide,division, subdivision || divide, subdivide ||divided, undivided, divisible, divisive
|-
| divorce, divorcee || divorce || divorced
|-
| do,doing || do, outdo, overdo,redo, undo || done, overdone, undone
|-
| doubt, doubter || doubt <br> /daʊt/ || undoubted,doubtful, doubtless || undoubtedly, doubtfully
|-
| dream, dreamer || dream (about) || dream, dreamless, dreamy || dream<span style="color:red">i</span>ly
|-
| dress, dresser, dressing || dress, redress, undress || dressed, undressed, dressy || dressily
|-
| drink, drinker, drinking, drunk, drunkenness || drink || drunk, drunken ||  drunkenly
|-
| drive,driver, driving || drive || driving ||
|-
| due,dues || due, undue  || duly, unduly
|}


* Bediene dafür die Schieberegler a, y<sub>s</sub> und x<sub>s</sub>, um dir die Eigenschaften der einzelnen Parameter ins Gedächtnis zu holen
== E ==


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
|earner, earnings || earn ||
|-
| earth || unearth || earthy || earthly, unearthly
|-
| ease,unease, easiness || ease || easy, uneasy || easily, uneasily
|-
| east, easterner || east, easterly, eastern, eastward(s)
|-
| economics,economist, economy || economize || economic, economical, uneconomic(al) || economically
|-
| education || educate || educated, uneducated, educational || educationally
|-
| effect,effectiveness, ineffectiveness || effect || effective,ineffective, ineffectual || effectively, ineffectively
|-
| effort || || effortless effortlessly ||
|-
| election, re-election, elector, electorate || elect, re-elect || unelected, electoral ||
|-
| electrician, electricity electric || electrify ||  electric, electrical || electrically
|-
| electronics || || electronic || electronically
|-
| embarrassment || embarrass || embarrassed, embarrassing || embarrassingly
|-
| emotion || || emotional, emotive || emotionally
|-
| emphasis || emphasize || emphatic || emphatically
|-
| employee,employer, employment, unemployment|| employ || unemployed ||
|-
| end, (happy) ending || end || unending, endless || endlessly
|-
| energy || energize || energetic || energetically
|-
| enjoyment || enjoy || enjoyable ||  enjoyably
|-
| enormity || || enormous || enormously
|-
| entrance, entrant, entry || enter ||  ||
|-
| entertainer, entertainment || entertain ||  entertaining ||  entertainingly
|-
| enthusiasm, enthusiast  || enthuse || enthusiastic, unenthusiastic || enthusiastically, unenthusiastically
|-
| environment, environmentalist || || environmental || environmentally
|-
| equality, inequality || equalize || equal, unequal ||  equally, unequally
|-
| escape,escapism || escape || escaped, inescapable || inescapably
|-
| essence,essentials || || essential|| essentially
|-
| estimate,estimation || estimate, overestimate, underestimate || estimated ||
|-
| event, non-event || || eventful, uneventful, eventual (=schließlich)|| eventfully, eventually
|-
| exam, examination, cross-examination, examiner || examine,cross-examine || ||
|-
| excellence || excel || excellent || excellently
|-
| excitement || excite || excitable, excited, exciting,unexciting || excitedly, excitingly
|-
| excuse || excuse || excusable, inexcusable || inexcusably
|-
| existence || exist, coexist || non-existent, existing, pre-existing ||
|-
| expectancy, expectation || expect || expectant, unexpected || expectantly, unexpectedly
|-
| expenditure,expense, expenses || expend || expensive, inexpensive || expensively, inexpensively
|-
| experience, inexperience || experience || experienced, inexperienced
|-
| experiment || experiment || experimental || experimentally
|-
| expert, expertise || || expert, inexpert || expertly
|-
| explaining, explanation || explain || unexplained, explanatory, explicable, inexplicable || inexplicably
|-
| explosion, explosive|| explode || exploding, explosive || explosively
|-
| exploration, explorer || explore|| exploratory ||
|-
| expression || express || expressive || expressively
|-
| extreme,extremism, extremist, extremity || || extreme, extremist || extremely
|}


<ggb_applet height="450" width="450" showResetIcon="true" id="hd52ksfn" />
== F ==


'''Lückentext! - Ordne die richtigen Begriffe zu:''' <br>  
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| fact || || factual || factually
|-
| fail, failure || fail || unfailing || unfailingly
|-
| fairness || || fair,unfair || fairly, unfairly
|-
| faith, faithfulness ||  ||faithful, unfaithful || faithfully
|-
| familiarity, family|| familiarize || familiar, unfamiliar || familiarly
|-
| fame || famed, famous, infamous || famously, infamously
|-
| fashion || fashion || fashionable, unfashionable || fashionably, unfashionably
|-
| fat || fatten || fat, fattening, fatty ||
|-
| fastener || fasten, unfasten || ||
|-
| fault || fault || faultless,faulty || faultlessly
|-
| fear || fear || fearful, fearless, fearsome || fearfully, fearlessly
|-
| feel, feeling || feel || unfeeling
|-
| fiction, nonfiction||  || fictional, fictive
|-
| fill, refill, filling|| fill (up), fill (in) , refill ||  filling
|-
| final, semifinal, finalist || finalize ||  final || finally
|-
| finish || finish || finished,unfinished
|-
| firmness,infirmity || ||  firm,infirm  ||firmly
|-
| fish,fishing || fish || fish || fishily
|-
| fit, fittings || fit || fitted, fitting || fittingly
|-
| fix, fixation, fixture|| fix || fixed, transfixed, unfixed ||
|-
| flat || flatten || flat || flatly
|-
| flower || flower || flowered/flowery, flowering
|-
| fold, folder || fold, unfold || folded, folding ||
|-
| follower, following || follow ||following
|-
| force || force || forceful, forcible || forcefully, forcibly
|-
| forest, deforestation, forestry || || forested ||
|-
| forgetfulness || forget || forgetful, unforgettable || forgetfully
|-
| forgiveness || forgive ||forgiving, unforgiving ||
|-
| form, formation, transformation, || form, reform, transform  || reformed reformer, transformer
|-
| formality || formalize || formal, informal || formally, informally
|-
| fortune ||    || fortunate, unfortunate || fortunately, unfortunately
|-
| freebie,freedom || free || free || free,freely
|-
| freeze,freezer || freeze || freezing, frozen ||
|-
| frequency, infrequency || frequent || frequent, infrequent || frequently, infrequently
|-
| freshness,refreshments || freshen, refresh || fresh, refreshing || freshly, refreshingly
|-
| friend, friendliness || befriend || friendly, unfriendly ||
|-
| fright  || frighten || frightened,frightening, frightful || frighteningly, frightfully
|-
| fruit, fruition ||  || fruitful, fruitless,fruity || fruitfully, fruitlessly
|-
| fund, refund, funding || fund, refund || funded ||
|-
| furnishings,furniture || furnish ||furnished, unfurnished ||
|}


<div class="lueckentext-quiz">
== G ==
Die Scheitelpunktsform mit dem Paramter a besitzt die Gleichung '''y = a[x - x<sub>s</sub>]<sup>2</sup> + y<sub>s</sub>'''. Die allgemeine Scheitelpunktsform wird dabei um den Parameter '''a''' erweitert. Dadurch kommt neben der '''Verschiebung''' der Parabel noch die '''Streckung, Stauchung und Spiegelung''' dazu. Ferner gilt festzuhalten, dass sowohl die Verschiebung der Parabel in der '''Ebene''', sowie die Veränderung durch den Vorfaktor a, '''unabhängig''' voneinander betrachtet werden.
</div>|3=Arbeitsmethode}}


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| garden, gardener, gardening || garden || ||
|-
| generalization || generalize || general || generally
|-
| generosity || || generous || generously
|-
| gentleness, gentleman ||  || gentle || gently
|-
| gladness||  gladden || glad || gladly
|-
| glass, glasses || || glassy ||
|-
| globe, globalization || || global || globally
|-
| good, goodies, goodness, goods || || good ||
|-
| government, governor || govern || governmental, governing || governmentally
|-
| gratitude,ingratitude ||  || grateful, ungrateful  || gratefully
|-
| greatness || || great || greatly
|-
| green, greenery, greens (vegetables), greenhouse-effect || || green || greenish, green
|-
| ground, underground, grounding, || ground || groundless, underground ||underground
|-
| grower, growth, undergrowth ||  grow, outgrow || growing, grown, overgrown  ||
|-
| guilt, guiltiness || || guilty || guiltily
|}
== H ==


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| habit, habitat ||  || habitual || habitually
|-
| hair, hairiness|| || hairless, hairy ||
|-
| hand, handful || hand (over) ||underhand, handy ||
|-
| handle,handler, handling || handle || ||
|-
| hanger hanging || hang, overhang || ||
|-
| happiness,unhappiness ||  happy, unhappy || happily, unhappily
|-
| hardship || harden ||hard || hard, hardly
|-
| harm, harmfulness || harm ||unharmed, harmful, harmless || harmlessly
|-
| head, heading, overheads || head, behead || overhead, heady  overhead
|-
| health || ||healthy, unhealthy|| healthily, unhealthily
|-
| hearing || hear, overhear (belauschen) ||unheard, unheard of
|-
| heart, heartlessness ||  || hearty, heartened, heartening, heartless || heartily, heartlessly
|-
| heat, heater, heating || heat, overheat  || heated,unheated  || heatedly
|-
| height, heights || heighten || heightened ||
|-
| help, helper, helpfulness, helping || help ||helpful, unhelpful, helpless || helpfully, helplessly
|-
| highness || high  ||high ||highly
|-
| historian, history || historic, prehistoric, historical || historically
|-
| hold, holder, holding || hold ||
|-
| home  || ||homeless, homely || home
|-
| honesty, dishonesty  || ||honest, dishonest  ||honestly, dishonestly
|-
| hope, hopefulness, hopelessness || hope || hopeful, hopeless hope || hopefully, hopelessly
|-
| human, humanism, humanity, inhumantiy || human,inhuman, superhuman, || humanly, humanely
|-
| hunger|| hunger ||  hungry ||hungrily
|-
| hurry || to hurry ||hurried, unhurried || hurriedly
|-
| hurt || hurt ||unhurt, hurtful || hurtfully
|}


Um die wichtigsten Eigenschaften aller Parameter zu wiederholen, lies den folgenden Merksatz und überprüfe, ob dir alle Eigenschaften klar sind.
== I ==


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| ice, icicle, icing || ice || icy || icily
|-
| identification, identity || identify ||  identifiable, unidentified ||
|-
| imagination|| '''imagine''' ||| imaginable, unimaginable, '''imaginary''' || unimaginably, imaginative imaginatively
|-
| importance ||  || important, unimportant || importantly
|-
| impression || impress || impressionable, impressive || impressively
|-
| improvement || improve ||  improved ||
|-
| increase || increase, decrease || increase|  increased ||  increasingly
|-
| credibility, incredulity ||  || incredible, credible, incredulous || incredibly, incredulously
|-
| independence, independent  || independent ||  independently
|-
| industrialist, industrialization, industry || industrial, industrialized, industrious || industrially, industriously
|-
| infection, disinfectant || infect, desinfect || infectious || infectiously
|-
| inflation || inflate, deflate || inflatable,inflated, inflationary
|-
| informant, information, informer || inform, misinform || informative, uninformative, informed, uninformed ||
|-
| injury || injure || injured, uninjured ||
|-
| innocence ||  || innocent ||innocently
|-
| insistence || insist on || insistent || insistently
|-
| instance,instant || || instant, instantaneous || instantly, instantaneously
|-
| instruction, instructor || instruct || instructive||  instructively
|-
| intelligence || || intelligent, unintelligent, intelligible, unintelligible  || intelligently
|-
| intent, intention || intend || intended, unintended, intentional, unintentional ||  intentionally, unintentionally
|-
| interest || interest in || interested, disinterested, uninterested, interesting || interestingly
|-
| interruption || interrupt || uninterrupted ||
|-
| interview, interviewee interviewer || interview ||||
|-
| introduction || introduct || introductory
|-
| invention, inventiveness, inventor || invent, reinvent || inventive  || inventively
|-
| invitation, invite || invite || uninvited, inviting ||  invitingly
|-
| involvement || involve in || involved, uninvolved ||
|-
| item || itemize || itemized


{{Box|1=Zusammenfassung|2=
|}
Für die quadratische Funktion '''"f(x)<math>=</math>a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>"''' gilt: 
* Für den Parameter a gilt:
** Der Parameter a sorgt für eine '''Streckung''', '''Stauchung''' und/oder '''Spiegelung''' der Parabel
** Für '''a > 1''' ist der Graph '''gestreckt''' und nach '''oben''' geöffnet
** Für '''0 < a < 1''' ist der Graph '''gestaucht''' und nach '''oben''' geöffnet
** Für '''a < -1''' ist der Graph '''gestreckt''' und nach '''unten''' geöffnet
** Für '''-1 < a < 0''' ist der Graph '''gestaucht''' und nach '''unten''' geöffnet


* Für den Parameter x<sub>s</sub> gilt:
** Der Parameter x<sub>s</sub> sorgt für eine '''Verschiebung''' entlang der x-Achse
** Für '''x<sub>s</sub> > 0''' gilt: Verschiebung nach '''rechts''' 
** Für '''x<sub>s</sub> < 0''' gilt: Verschiebung nach '''links''' 


* Für den Parameter y<sub>s</sub> gilt:
== J ==
** Der Parameter y<sub>s</sub> sorgt für eine '''Verschiebung''' auf der y-Achse
** Für '''y<sub>s</sub> > 0''' gilt: Verschiebung nach '''oben'''
** Für '''y<sub>s</sub> < 0''' gilt: Verschiebung nach '''unten'''
|3=Merksatz}}


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| joke, joker || joke || || jokingly
|-
| journal, journalism, journalist || || journalistic ||
|-
| judge,judg(e)ment || judge || judgmental ||
|-
| juice, juices ||  || juicy||
|}


==STATION 2: Aufgaben zu "f(x) <math>=</math> a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>"==
== K ==


{{Box|1=Ordne den Graphen die richtige Funktionsvorschrift|2=Du siehst hier sowohl ein paar Graphen, als auch ein paar Funktionsvorschriften der Form
{|class="wikitable"
"f(x) <math>=</math> a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>". Versuche die jeweils richtigen Pärchen zu finden.
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| keenness ||  || keen (on) ||  keenly
|-
| keep, keeper, keeping|| keep || kept
|-
| kill, overkill, killer, killing || kill ||  ||
|-
| kindness,unkindness || kind, unkind || kindly, unkindly
|-
| knowledge  || know || knowing, knowledgeable, known, unknown || knowingly, unknowingly,knowledgeably
|}


<div class="lueckentext-quiz">
== L ==
{{{!}}
{{!}}-
{{!}} [[Bild:Parabelkeins.png|180px]]  {{!}}{{!}}{{!}}{{!}}  [[Bild:Parabelkzwei.png|180px]]  {{!}}{{!}}{{!}}{{!}}  [[Bild:Parabelkdrei.png|180px]]  {{!}}{{!}}{{!}}{{!}}  [[Bild:Parabelkvier.png|180px]]  {{!}}{{!}}{{!}}{{!}}  [[Bild:Parabelkfünf.png|180px]]
{{!}}-
{{!}} <strong> y = [x - 2,5]<sup>2</sup> - 1,5 </strong>  {{!}}{{!}}{{!}}{{!}} <strong> y = -4[x + 2]<sup>2</sup> + 1 </strong> {{!}}{{!}}{{!}}{{!}} <strong> y = [x + 3,5]<sup>2</sup>  </strong> {{!}}{{!}}{{!}}{{!}} <strong> y = 5[x + 2,5]<sup>2</sup> + 2 </strong> {{!}}{{!}}{{!}}{{!}} <strong> y = 2[x - 4]<sup>2</sup> - 3 </strong>
{{!}}}</div>|3=Arbeitsmethode}}


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| enlargement || enlarge || large || largely
|-
| laugh, laughter || laugh || laughable || laughably
|-
| law, lawyer, outlaw || outlaw || lawful, unlawful || lawfully, unlawfully
|-
| laziness ||  || lazy || lazily
|-
| lead, leader, leadership || lead ||  leading, lead
|-
| learner, learning || learn ||  learned, unlearned ||
|-
| legality, illegality, legalization || legalize || legal, illegal || legally, illegally
|-
| length, longitude | lengthen || lengthy, lengthening || lengthily
|-
| liar, lie || lie || lying
|-
| life, liveliness, living|| live, outlive, relive || lifeless, lifelike, lifelong || lifelessly live (on TV), lively
|-
| light, lighter, lighting, lightening, lightness|| light, lighten || light || lightly
|-
| dislike, liking|| like, dislike || likeable ||
|-
| likelihood || ||likely, unlikely ||likely
|-
| limit, limitation, limitations || limit || limited, unlimited
|-
| literature, literacy || || literary, literate, illiterate
|-
| local, location, relocation || dislocate, relocate || local || locally
|-
| looseness || loosen (the knot) || (drive on ) loose gravel || (He broke) loose.
|-
| loser, loss || lose  || lost ||
|-
| loudness || || aloud, loud/loudly
|-
| love,lover || love || lovable, unlovable, loveless, lovely || lovingly
|-
| low ||  lower || low, lower, lowly || low
|-
| luck || lucky, unlucky || luckily, unluckily
|}


Ich nehme an, dass das kein Problem für dich war. Bei dieser Aufgabe war es nämlich noch nicht nötig den Vorfaktor a zu bestimmen. 
== M ==


Jetzt wollen wir das Ganze ein wenig erschweren!  
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| machine, machinery, machinist, mechanic, mechanics,mechanism ||    || mechanical, mechanized  || mechanically
|-
|| magic, magician || do magic || magic, magical || magically
|-
| make, remake, maker, || make, remake || making unmade
|-
| man, manhood, mankind, manliness, || man || manly, manned, unmanned, mannish || mannishly, manfully
|-
| management, manager, manageress || manage || manageable,unmanageable, managerial
|-
| mark,marker, markings || mark || marked, unmarked || markedly
|-
| market, marketing, marketability, marketer, marketeer || market || marketable
|-
| marriage || marry, remarry ||  married, unmarried, marriageable ||
|-
| match, mismatch || match || matching, unmatched, matchless || matchlessly
|-
| material, materialism, materialist, || materialize || immaterial, materialistic  || materially
|-
| meaning, meaningfulness ||'''mean''' || meaningful, meaningless ||  meaningfully, meaninglessly
|-
| measure,measurement || measure || measurable, immeasurable,measured || immeasurably
|-
| medical, medication, medicine ||  to medicate || medical, medicated, medicinal, || medically, medicinally
|-
| memorial, memory || memorize || memorable ||  memorably
|-
| mentality ||  || mental  || mentally
|-
| method, methodology ||  || methodical, methodological || methodically
|-
| militancy, militant, the military, militarist, militia,  ||  military, militant,militaristic, demilitarized  || militantly,militarily
|-
| mind, minder, reminder, mindlessness || '''mind''', '''remind''' ||  mindless,mindful || mindlessly
|-
| minimum, minimization, minimalist || minimize  || minimal, minimum ||    minimally
|-
| miss, near-miss ||  miss || missing ||
|-
| mistake || mistake || mistaken, unmistakable || unmistakably, mistakenly
|-
| mix, mixer, mixture || mix || mixed ||
|-
| modernity, modernization || modernize || modern, modernistic
|-
| moment ||  || momentary, momentous || momentarily
|-
| mood, moodiness ||  || moody || moodily
|-
| moral, morals, morality, immorality || moralize || moral, amoral, immoral, moralistic  || morally
|-
| mother, motherhood || mother || || motherly
|-
| move,movement, removal, movers (and shakers), remover, || '''move''', remove  || movable, unmoved, moving|| movingly
|-
| murder, murderer || murder || murderous || murderously
|-
| music, musical, musician, musicality ||  || musical,unmusical || musically
|}


Kannst du dich noch erinnern, wie man den Vorfaktor a bestimmt?
== N ==


{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| name || name, rename || named, unnamed, nameless || namely
|-
| nation, national, multinational,nationalism, nationalist, nationality, nationalization || nationalize  || national, international, multinational, nationalistic ||  nationally, internationally
|-
| nature, naturalist, naturalization, naturalness the supernatural, || naturalize || natural, supernatural,  unnatural, naturalistic  || naturally, unnaturally
|-
| necessity || necessitate || necessary, unnecessary || necessarily, unnecessarily
|-
| need, needs || need || needless, needy, needed || needlessly
|-
| nerve,nerves, nervousness ||  unnerve || nervous, nervy, nerveless, unnerving ||  nervously, nervelessly, unnervingly
|-
| news, renewal, newness || renew || new,renewable, renewed  || newly, anew
|-
| night, midnight overnight, ||  || nightly, nights
|-
| noise, noisiness ||  || noisy, noiseless  || noisily
|-
| normality/normalcy ([[amerikanisches Englisch|AmE]]), abnormality, norm || normalize ||  normal, abnormal || normally, abnormally
|-
| north, northerner ||  || north, northerly, northern, north, northward(s), northbound
|-
| notice  ||notice || noticeable, unnoticed || noticeably
|-
| number, numeral ||  number, outnumber, enumerate|| innumerable, numerical, numerous, numbered
|-
| nurse, nursery, || nurse  || nursing ||
|}


{{Box|1=Finde zu den zwei Graphen die passende Funktionsvorschrift!|2=
== O ==


Falls du nicht genau weißt, wie du vorgehen sollst, schau dir die Hilfe an!
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| obedience,disobedience || obey, disobey || obedient, disobedient  || obediently, disobediently
|-
| occasion ||  || occasional || occasionally
|-
| offence/offense ([[Amerikanisches Englisch|AmE]]), offender, offensive ||  offend  || offensive, inoffensive || offensively
|-
| office, officer, official, officialdom  || officiate || official, unofficial  || officially, unofficially
|-
| the open, opener, opening,openness || open || open, opening || openly
|-
| operation, cooperation, operative, cooperative,operator || operate, cooperate || operational, operative, cooperative, operable || operationally
|-
| opposition, opposite || oppose || opposed, opposing, opposite || opposite
|-
| option || opt (out) / (for) || optional || optionally
|-
| order, disorder || order || ordered, disordered || orderly, disorderly
|-
| organization, disorganization, reorganization, organizer || organize, reorganize ||  organizational, organized, disorganized
|-
| origin, original, originality || originate || original, unoriginal  || originally
|-
| owner, ownership || own, disown || ||
|}


== P ==


[[Bild:ParabelAufgabe2Station2-2.jpg|center]]
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| pack, package, packaging, packet, packing, packer || pack, unpack || packed  package
|-
| pain || pain || pained, painful, painless || painfully, painlessly
|-
| paint, painter, painting || paint || ||
|-
| part, counterpart, parting, partition || depart, impart,  part || partial, parting, impartial part ||  partially, partly
|-
| pass,overpass, underpass,passage, passing, passing || pass || passable
|-
| patience,impatience, patient || ||  patient,impatient || patiently, impatiently
|-
| pay, payment, repayment, payee, payer, payoff, payback, payout || pay, repay || pa<span style="color:red">i</span>d, unpa<span style="color:red">i</span>d, underpa<span style="color:red">i</span>d ||
|-
| peace || pacify || peaceful  || peacefully
|-
| perfection, imperfection, perfectionist, perfectionism || perfect || perfect, imperfect || perfectly
|-
| performance, performer || perform || performant
|-
| permission, permi<span style="color:red">t</span>, permissiveness || permit || permissible,impermissible, permissive ||
|-
| person, personality || personalize, personify || personal, impersonal, personalized, || personally
|-
| persuasion, persuasiveness || persuade, dissuade  || persuasive || persuasively
|-
| photo, photograph, photographer, photography || photograph || photogenic, photographic ||
|-
| picture  || picture || pictorial, picturesque ||
|-
| place, placement, displacement, replacement || place, displace, replace || misplaced
|-
| plan, planner, planning || plan || unplanned ||
|-
| plant, transplant, plantation, planter || plant, transplant||
|-
| play, interplay, replay, player,playfulness,playback, playoff ||  play, outplay, replay, downplay, || playful, playable  || playfully
|-
| pleasantry, pleasure, displeasure  || please, displease || pleasant, unpleasant, pleased, displeased, pleasing, pleasurable || pleasantly, unpleasantly
|-
| poem, poet, poetry || || poetic || poetically
|-
| point, pointer, pointlessness || point || pointed, pointless, pointy ||  pointlessly, pointedly
|-
| politeness || || polite, impolite || politely, impolitely
|-
| politician, politics, politicking ||  politicize || political, politicized || politically
|-
| popularity, unpopularity, popularization || popularize  || popular, unpopular || popularly
|-
| population || populate || populated, unpopulated, populous ||
|-
| possibility, impossibility, the impossible || possible, impossible || possibly, impossibly
|-
| post, postage || post || postal||
|-
| power, superpower, powerlessness || power, empower, overpower ||  powerful, overpowering, powerless || powerfully
|-
| practical, practicalities, practicality, practicability ||  || practicable,practical, impractical || practically
|-
| practice, practitioner || practice/practise ([[Amerikanisches Englisch|AmE]]) ||practised/practiced, practising/practicing
|-
| precision || || precise, imprecise || precisely
|-
| preference || prefer || preferable, preferential, prefe<span style="color:red">rr</span>ed || preferably
|-
| preparation, preparations, preparedness, {{wpen|prepper}}|| prepare || prepared, unprepared, preparatory ||
|-
| presence,present, presentation, presenter || present, represent || present, presentable || presently
|-
| press,pressure || press, pressure/pressurize, depress,repress || pressed, pressing, pressurized ||
|-
| prevention | prevent (from) || preventable, preventive/preventative ||
|-
| price || price || overpriced, priceless, pricey/pricy ||
|-
| print, printer, printing || print || printed, printable ||
|-
| prison, prisoner, imprisonment || imprison|| ||
|-
| privacy, private, privatization || privatize ||  private || privately
|-
| probability || || probable, improbable || probably,improbably
|-
| process, processing, procession, processor || process || processed, processional ||
|-
| produce,producer, product, production, reproduction, productivity || produce, reproduce ||  productive,counterproductive, unproductive, reproductive, unproductive || productively
|-
| profession, professional || ||  professional, unprofessional || professionally
|-
| profit,profitability, profiteer, profiteering || profit || profitable, unprofitable || profitably
|-
| progress, progression || progress ||  progressive || progressively
|-
| proof || prove, disprove || proven, unproven,  water-proof ||
|-
| protection, protector, protectionism, protectorate || protect || protected, unprotected, protective, || protectively
|-
| provider, provision, provisions || provide || provisional || provisionally
|-
| public, publication, publicist, publicity || publicize ||  public ||  publicly
|-
| publisher, publishing || publish || published, unpublished ||
|-
| punishment, punisher || punish || punishable, punishing || punishingly
|-
| purification, purist, purity, impurity, purifier|| puriy || pure, impure || purely
|-
| purpose, purposelessness || repurpose || purposeful, purposeless || purposefully, purposely, purposelessly
|-
| push, pusher, pushiness || push || pushed, pushy ||
|}


'''Wie ist dein Ergebnis:'''
== Q ==


<div class="multiplechoice-quiz">
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| qualification, disqualification, qualifier || qualify, disqualify || qualified, unqualified ||
|-
| quarter, quarters || quarter || quarterly  || quarterly
|-
| question, questioning, questioner, questionnaire  || question || questionable, unquestionable || unquestionably
|-
| quiet, disquiet || quieten/quiet  || quiet || quietly
|}


'''1. Wie lautet die richtige Funktionsgleichung für den Graph a?''' (!y <math>=</math> 1[x - 4]<sup>2</sup> - 3) (!y <math>=</math> 3[x – 4]<sup>2</sup> + 3) (y <math>=</math> 2[x – 4]<sup>2</sup> - 3)</div>
== R ==


<div class="multiplechoice-quiz">
{|class="wikitable"
|-
!<big>Nouns</big> !! <big>Verbs</big> !! <big>Adjectives</big> !! <big>Adverbs</big>
|-
| race, racism, racist || race || racial, multiracial, racist  || racially
|-
| rarity || || rare, rarefied, rarified || rarely
|-
| rate, rating, ratings || rate, underrate || overrated, underrated ||
|-
| reaction, reactor, reactant || react, overreact|| reactionary ||
|-
| read, reader, readership, reading || read || readable, unreadable ||
|-
| readiness || ready || ready ||readily
|-
| realism, realist, reality, unreality, realization  || realize || real, unreal, realistic, unrealistic, realisable || real, really, realistically
|-
| reason, reasoning, reasonableness || reason || reasonable, unreasonable, reasoned || reasonably, unreasonably
|-
| receipt, receipts, receiver, reception, receptive, recipient, reciprocity || receive || reciprocal, received ||  reciprocally
|-
| recognition || recognize || recognizable, unrecognizable ||  recognizably
|-
| record, recorder, recording || record || recorded, unrecorded ||
|-
| referee, reference, referral || refer, referee || referred ||
|-
| reflection, reflector || reflect || reflective || reflectively
|-
| regret || regret || regrettable, regretful || regrettably, regretfully
|-
| regular, regularity, irregularity || regulate || regular, irregular || regularly, irregularly
|-
| relation, relative, relationship || relate ||  related, unrelated, relative || relatively
|-
| relaxation || relax ||  relaxed,relaxing ||
|-
| reliability, reliance || rely (on) || reliable, unreliable, reliant || reliably
|-
| religion || || religious, irreligious || religiously
|-
| the remainder, remains || remain ||  remaining ||
|-
| remark || remark || remarkable, unremarkable || remarkably
|-
| repair, disrepair || repair || irreparable || irreparably
|-
| repeat, repetition || repeat || repeated, repetitive/repetitious || repeatedly, repetitively
|-
| report, reporter || report ||  unreported || reportedly
|-
| representation, representative || represent || representative, unrepresentative || represent
|-
| reputation, disrepute  ||  reputable, disreputable, reputed || reputedly, reputably
|-
| respect, disrespect, respectability, respects || respect || respectable, respected, respectful, disrespectful, respective ||  respectably, respectfully,| respectively, disrespectfully
|-
| respondent, response, responsiveness, first-responder || respond || respresponsive,unresponsive || responsively
|-
| responsibility, irresponsibility || || responsible, irresponsible || responsibly, irresponsibly
|-
| rest, unrest, restlessness, restaurant, rest-room || rest || restless, rested, restful restive ||  restlessly
|-
| retiree,retirement || reitre || retired, retiring ||
|-
| reward || reward || rewarding,unrewarding ||
|-
| riches,richness, enrichment, the rich || enrich || rich || richly
|-
| ride,rider, || ride, override || riding overriding, riderless ||
|-
| right, rightness, rights, righteousness, || rigth || right, righteous, rightful, rightist || right, rightly, rightfully|-
|-
| roll, roller ||roll, unroll|| ||
|-
| romance,romantic, romanticism || romance, romanticize || romantic, unromantic, romanticized || romantically
|-
| rough, roughage, roughness || rough, roughen (somenone up) ||rough || roughly
|-
| round, rounders, roundness || round || round, rounded || round, roundly
|-
| royal, royalist, royalty ||||royal, royalist || royally
|-
| rudeness || || rude || rudely
|-
| rule, ruler, ruling, unruliness || rule, overrule || ruling, unruly  ||
|-
| run, rerun, runner, running, rundown || run, outrun, overrun || running, runny
|}


'''2. Wie lautet die richtige Funktionsgleichung für den Graph b?''' (!y <math>=</math> -2[x + 2]<sup>2</sup> + 1) (y <math>=</math> -4[x + 2]<sup>2</sup> + 1) (!y <math>=</math> -0,5[x + 2]<sup>2</sup> + 1)</div>
[[Kategorie:Englisch]]
|3=Arbeitsmethode}}
 
'''Hilfe:''' <br>
{{Box|1=Anleitung zur Bestimmung des Vorfaktors a|2=
* Der Startpunkt zum Bestimmen des Vorfaktors ist der Scheitelpunkt<br>
* Gehe auf der x-Achse eine Einheit nach rechts <br>
* Bestimme in y-Richtung die Anzahl der Einheiten bis zur Parabelkurve <br>
* Die Anzahl der Einheiten ergibt den Wert vom Vorfaktor a <br>
* Hat man die Einheiten nach oben abgezählt, dann ist der Wert von a positiv <br>
* Hat man die Einheiten nach unten abgezählt, dann ist der Wert von a negativ  <br>
|3=Merksatz}}
 
 
{{Box|1=Betrachte die Funktionsvorschriften genau und kreuze die richtigen Aussagen an!|2=
Achtung! Es können auch mehrere Antworten richtig sein!
 
<div class="multiplechoice-quiz">
 
'''"f(x) <math>=</math> -2x<sup>2</sup> + 5"''' (!Die Parabel ist nach oben geöffnet)(Die Parabel ist nach unten geöffnet)(Die Parabel hat den höchsten Punkt bei <math>[0 \vert 5]</math>) (Die Parabel ist gestreckt) (!Die Parabel ist gestaucht) (!Die Parabel ist um 2 Einheiten nach links verschoben)
 
'''"f(x) <math>=</math> (x - 3)<sup>2</sup> - 2"''' (!Die Parabel ist gestaucht)(Die Parabel hat den tiefsten Punkt bei <math>[0 \vert -2]</math>)(Die Parabel verläuft durch den Punkt <math>[0 \vert 7]</math>) (!Die Parabel ist um 3 Einheiten nach links verschoben) (Die Parabel ist kongruent zur Normalparabel) (Die Parabel ist um 3 Einheiten nach rechts verschoben)
 
'''"f(x) <math>=</math> 6 + 2 (x + 2)<sup>2</sup>"''' (!Die Parabel ist nach unten geöffnet)(!Die Parabel wurde um 2 Einheiten nach rechts verschoben)(Die Parabel ist nach oben geöffnet ) (Die Parabel wurde um 2 Einheiten nach links verschoben) (!Die Parabel ist gestaucht) (Die Parabel ist gestreckt)
 
'''Die gestreckte Parabel ist um 2 Einheiten nach links und um 4 Einheiten nach oben verschoben''' (!y <math>=</math> 4 [x - 2]<sup>2</sup> - 4)(!y <math>=</math> 0,2 [x - 2]<sup>2</sup> + 4)(!y <math>=</math> 2 [x - 2]<sup>2</sup> + 4)(y <math>=</math> 3 [x + 2]<sup>2</sup> + 4)(!y <math>=</math> 0,5 [x + 2]<sup>2</sup> - 4)(!y <math>=</math> 5 [x + 2]<sup>2</sup> - 4)(!y <math>=</math> 0,8 [x - 2]<sup>2</sup> + 4)(y <math>=</math> 1,77 [x + 2]<sup>2</sup> + 4)
</div>|3=Arbeitsmethode}}
 
 
 
{{Box|1=Kniffelaufgabe|2=
<div class="multiplechoice-quiz">
 
'''Welche der folgenden Funktionsvorschriften hat eine Nullstelle? Achtung! Die Aufgabe ist nur durch logisches Denken zu lösen, es ist keine Rechnung erforderlich!''' (y <math>=</math> 2 [x – 3]<sup>2</sup> - 2) (!y <math>=</math> 2 [x + 5]<sup>2</sup> + 1 ) (y <math>=</math> - [x + 1]<sup>2</sup> + 2) (!y <math>=</math> -3 [x – 1]<sup>2</sup> -1)
</div>
 
 
'''Hilfe:''' <br>
Falls du Hilfe brauchst, kannst du dir hier einen Tipp holen!<br>
{{Lösung versteckt|Eine Nullstelle ist der Punkt, an dem der Graph die x-Achse schneidet!|2=Hilfe anzeigen|3=Hilfe ausblenden}}
 
 
'''Lösung:'''<br>
{{Lösung versteckt|
[[Bild:ParabelStation2Aufgabe4.jpg|center]]
Die richtigen Lösungen sind y <math>=</math> 2 [x – 3]<sup>2</sup> - 2 und y <math>=</math> - [x + 1]<sup>2</sup> + 2, deren Graphen farbig hervorgehoben sind. <br>
Wie du in der Grafik erkennen kannst, kommt es nur auf den Parameter y<sub>s</sub> und den Vorfaktor a an. <br>
Ist der Vorfaktor a positiv und der Parameter y<sub>s</sub> zugleich negativ, so liegt der Scheitelpunkt der nach oben geöffneten Parabel unterhalb der x-Achse. <br>
Durch diese Gegebenheit schneidet die Parabel die x-Achse ab einem bestimmten Wert für x.
<br>
Genau umgekehrt verhält es sich für den Fall, dass der Vorfaktor a negativ und der Parameter y<sub>s</sub> positiv ist.}}|3=Arbeitsmethode}}
 
 
==STATION 3: Die Normalform und der Parameter a==
 
Auch bei der Normalform ändert sich bei Hinzunahme des Vorfaktors a nicht viel.
 
Wieder kommt es darauf an, die Normal- in die Scheitelpunktsform und umgekehrt, die Scheitelpunkts- in die Normalform umzuformen.
 
Wir betrachten zunächst die Umformung von der Scheitelpunkts- zur Normalform.
 
 
===Von der Scheitelpunkts- zur Normalform===
 
Da es sich genauso verhält wie im Lernpfad "Die Normalform f(x) <math>=</math> x<sup>2</sup> + bx + c" gezeigt, wirst du die Umformung wieder selbst durchführen.
 
 
{{Box|1=Bringe f(x) <math>=</math> 2(x - 3)<sup>2</sup> - 4 in die Normalform|2=
 
Du hast die Scheitelpunktsform '''"f(x) <math>=</math> 2(x - 3)<sup>2</sup> - 4"''' gegeben.
Diese Form soll nun durch '''"Ausmultiplizieren"''' und '''"Zusammenfassen"''' der Terme <br>
auf die Form '''"f(x) <math>=</math> ax<sup>2</sup> + bx + c"''' gebracht werden.
 
Du hast die einzelnen Terme vorgegeben, bring sie in die richtige Reihenfolge!
 
<div class="lueckentext-quiz">
{{{!}}
{{!}}-
{{!}} y<math>=</math>  {{!}}{{!}} a[x - x<sub>s</sub>]<sup>2</sup> + y<sub>s</sub> <br> 
{{!}}-
{{!}} y<math>=</math>  {{!}}{{!}} <strong> 2[x - 3]<sup>2</sup> -  4 </strong> <br> 
{{!}}-
{{!}} y<math>=</math> {{!}}{{!}} <strong> 2[x<sup>2</sup> - 6x + 9] - 4 </strong> <br>
{{!}}-
{{!}} y<math>=</math> {{!}}{{!}} <strong> 2x<sup>2</sup> - 12x + 14 </strong> <br>
{{!}}-
{{!}} y<math>=</math> {{!}}{{!}} <strong> ax<sup>2</sup> + bx + c  </strong> <br>
{{!}}}
</div>|3=Arbeitsmethode}}
 
 
{{Box|1=Von der Scheitelpunktsform zur Normalform|2=
Die Normalform "f(x) <math>=</math> ax<sup>2</sup> + bx + c" entsteht aus der Scheitelpunktsform "f(x) <math>=</math> a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>" durch '''"Ausmultiplizieren"''' und '''"Zusammenfassen"''' der Terme.|3=Merksatz}}
 
 
Betrachten wir nun die andere Richtung.
 
 
===Von der Normal- zur Scheitelpunktsform===
 
Diese Umformung funktioniert genauso, wie das im Lernpfad '''"Die Normalform f(x) = x<sup>2</sup> + bx + c"''' gezeigte Verfahren. Mittels quadratischer Ergänzung gelangt man zur Scheitelpunktsform.
 
Zur Wiederholung, klicke dich durch die folgende Anleitung:<br>
<br>
 
1. Schritt: Gegeben ist die Parabel p <br>
{{Lösung versteckt|1=[[Bild:UmformungSchritt1.jpg]]|2=1. Schritt einblenden|3=Schritt ausblenden}}
 
 
2. Schritt: Faktor ausklammern <br>
{{Lösung versteckt|1=[[Bild:UmformungSchritt2.jpg]]|2=2. Schritt einblenden|3=Schritt ausblenden}}
 
 
3. Schritt: Quadratische Ergänzung<br>
{{Lösung versteckt|1=[[Bild:UmformungSchritt3.jpg]]|2=3. Schritt einblenden|3=Schritt ausblenden}}
 
 
 
4. Schritt: Binom erzeugen<br>
{{Lösung versteckt|1=[[Bild:UmformungSchritt4.jpg]]|2=4. Schritt einblenden|3=Schritt ausblenden}}
 
 
 
5. Schritt: Äußere Klammer auflösen<br>
{{Lösung versteckt|1=[[Bild:UmformungSchritt5.jpg]]|2=5. Schritt einblenden|3=Schritt ausblenden}}
 
 
 
6. Schritt: Scheitelkoordinaten<br>
{{Lösung versteckt|1=[[Bild:UmformungSchritt6.jpg]]|2=6. Schritt einblenden|3=Schritt ausblenden}}
 
Um das ein wenig einzuüben, löse die folgende Aufgabe!
 
 
 
{{Box|1=Zuordnung von Funktionsvorschrift, Graph und Scheitelpunkt|2=
 
Nimm dir ein Blatt und einen Stift zur Hand und stelle zu den vorgegebenen quadratischen Funktionen die Scheitelpunktsform auf. Ordne anschließend die entsprechenden Scheitelpunktsformen, Scheitelkoordinaten und Graphen den entsprechenden Funktionsgleichungen zu.
 
<div class="zuordnungs-quiz">
{{{!}}
{{!}} f(x) = 2x<sup>2</sup> + 12x + 14 {{!}}{{!}} f(x) = 2(x + 3)<sup>2</sup> - 4  {{!}}{{!}}  S[-3,-4] {{!}}{{!}} [[Bild:Station3AufgabeZuordnung1.jpg]] {{!}}{{!}}
{{!}}-
{{!}} f(x) = -3x<sup>2</sup> + 24x -41 {{!}}{{!}} f(x) = -3(x - 4)<sup>2</sup> + 7  {{!}}{{!}}  S[4,7] {{!}}{{!}} [[Bild:Station3AufgabeZuordnung2.jpg]] {{!}}{{!}}
{{!}}-
{{!}} f(x) = x<sup>2</sup> - 2x - 2 {{!}}{{!}} f(x) = (x - 1)<sup>2</sup> - 3  {{!}}{{!}} S[1,-3]{{!}}{{!}} [[Bild:Station3AufgabeZuordnung3.jpg]]
{{!}}}
</div>
 
'''Lösung quadratische Ergänzung:'''<br>
Falls du Probleme mit der quadratischen Ergänzung hattest, kannst du sie dir hier anschauen! <br>
{{Lösung versteckt|1=
      f(x) = 2x<sup>2</sup> + 12x + 14
          = 2 [x<sup>2</sup> + 6x] + 14
          = 2 [x<sup>2</sup> + 6x + 3<sup>2</sup> - 3<sup>2</sup>] + 14
          = 2 [(x + 3)<sup>2</sup> - 3<sup>2</sup>] + 14
          = 2 (x + 3)<sup>2</sup> - 2(3<sup>2</sup>) + 14
          = 2 (x + 3)<sup>2</sup> - 18 + 14
          = 2 (x + 3)<sup>2</sup> - 4
 
      f(x) = -3x<sup>2</sup> + 24x - 41
          = -3 [x<sup>2</sup> - 8x] - 41
          = -3 [x<sup>2</sup> - 8x + 4<sup>2</sup> - 4<sup>2</sup>] - 41
          = -3 [(x - 4)<sup>2</sup> - 4<sup>2</sup>] - 41
          = -3 (x - 4)<sup>2</sup> -[-3(-4<sup>2</sup>)] - 41
          = -3 (x - 4)<sup>2</sup> + 48 - 41
          = -3 (x - 4)<sup>2</sup> + 7
 
      f(x) = x<sup>2</sup> - 2x - 2
          = (x - 1)<sup>2</sup> - 1<sup>2</sup> - 2
          = (x - 1)<sup>2</sup> - 3
}}|3=Arbeitsmethode}}
 
 
Jetzt kennst und kannst du wirklich alles zur quadratischen Funktion.
Stelle dein Wissen in der vierten und letzten Station unter Beweis.
Hier wird alles zuvor Erlernte, in vermischten Aufgaben, abgefragt.
Viel Erfolg!
 
 
==STATION 4: Vermischte Aufgaben zur quadratischen Funktion==
 
{{Box|1=Finde die unverdrehte Lösung zu den verdrehten Wörtern!|2=
 
Du kannst deine Ergebnisse erst überprüfen, wenn alle Felder ausgefüllt sind!
 
<div class="schuettel-quiz">
 
Eine Funktion der Form "f(x) = ax<sup>2</sup> + bx + c" nennt man '''quadratische''' Funktion. <br>
 
Durch Umformen, mit Hilfe der quadratischen '''Ergänzung''', erhält man die '''Scheitelpunktsform''' "f(x) = a(x - x<sub>s</sub>)<sup>2</sup> + y<sub>s</sub>". <br>
 
Anhand der Scheitelpunktsform kann man die '''Koordinaten''' für den '''Scheitelpunkt''' ablesen. <br>
 
Der Scheitelpunkt gibt dabei den '''höchsten''' oder '''tiefsten''' Punkt der Parabel an. <br>
 
Hat die Parabel einen höchsten Punkt, so ist sie nach '''unten''' geöffnet und der Parameter a ist '''negativ'''. <br>
 
Ist der Vorfaktor hingegen positiv, so besitzt die Parabel einen '''tiefsten''' Punkt und die Parabel ist nach '''oben''' geöffnet. <br>
 
Außerdem bewirkt der Parameter a eine '''Streckung, Stauchung''', und/oder eine "Spiegelung" der Parabel. <br>
 
Nimmt der Vorfaktor einen Wert zwischen -1 und +1 an, so wird die Parabel '''gestaucht'''. <br>
 
Ist hingegen der Vorfaktor a kleiner -1 oder größer +1, so wird die Parabel '''gestreckt'''. <br>
Neben der Streckung und Stauchung der Parabel durch den Parameter a, existieren noch die Parameter x<sub>s</sub> und y<sub>s</sub>, die für eine '''Verschiebung''' der Parabel in der '''Ebene''' verantwortlich sind. <br>
 
Für y<sub>s</sub> > 0 wird die Parabel nach '''oben''' und für y<sub>s</sub> < 0 nach '''unten''' verschoben. <br>
 
Ähnlich verhält es sich bei dem Parameter x<sub>s</sub>, der für eine Verschiebung der Parabel in x-Richtung sorgt. <br>
 
Hier wird für x<sub>s</sub> > 0 nach '''rechts''' und für x<sub>s</sub> < 0 nach '''links''' verschoben.
 
</div>||3=Arbeitsmethode}}
 
 
 
{{Box|1=Kniffelaufgabe|2=
Gegeben ist die Funktion "f(x) = 0,5x<sup>2</sup> - x - 2,5" <br>
 
<div class="multiplechoice-quiz">
'''In welchem Punkt schneidet die Parabel die y-Achse und wie bestimmt man ihn?'''
(!Man kann die Koordinaten nur mittels quadratischer Ergänzung bestimmen)
(Schnittpunkt mit y-Achse: <math>[0 \vert -2,5]</math>)   
(Durch Einsetzen des bekannten x-Wertes bestimmt man den y-Wert)
(!Schnittpunkt mit y-Achse: <math>[1 \vert 2,5]</math>)
</div>
 
 
'''Tipp!''' <br>
{{Lösung versteckt|1=Überlege dir, was gelten muss, wenn die Parabel die y-Achse schneidet.|2=Tipp einblenden|2=Tipp ausblenden}}
 
'''Tipp!:''' <br>
{{Lösung versteckt|
Du kennst einen Koordinantenpunkt. An der Stelle, an der die Parabel die y-Achse schneidet, ist der x-Wert 0. Setze diesen Wert in die Gleichung ein und bestimme den zugehörigen y-Wert.|2=Tipp einblenden|2=Tipp ausblenden}}
 
'''Erklärung:''' <br>
{{Lösung versteckt|1=
Wenn die Parabel die y-Achse schneidet ist der y-Wert vorgegeben, er ist 0. Diesen Wert setzt man in die Funktionsgleichung ein und bestimmt den y-Wert.
y = 0,5x<sup>2</sup> - x - 2,5     
y = 0,5(0)<sup>2</sup> - 0 - 2,5
y = -2,5
 
|2=Erklärung einblenden|3=Erklärung ausblenden}}
 
 
 
{{Box|1=Quiz|2=
Finde die richtigen Lösungen! Es können auch mehrere Antworten möglich sein!'''
 
<div class="multiplechoice-quiz">
 
'''Für die Funktion "f(x) <math>=</math> x<sup>2</sup> + 2" gilt:''' (Die Parabel schneidet die y-Achse)(!Die Parabel schneidet die x-Achse)(Die Parabel hat den Scheitelpunkt S <math>[0|2]</math>) (!Die Parabel hat den Scheitelpunkt S <math>[2|0]</math>) (!Der Scheitelpunkt, ist der Punkt, an dem die Parabel die x-Achse schneidet)
 
 
'''Diese Funktion ist keine quadratische Funktion:''' (!y <math>=</math> [x - 2]<sup>2</sup>)(!y <math>=</math> 2x<sup>2</sup> + 3 - 5x)(y <math>=</math> 2x<sup>3</sup> + 2x + 3) (y <math>=</math> 8 + 2x) (!y <math>=</math> [x + 3][x - 3])
 
 
'''Für die Funktion "f(x) <math>=</math> 2x<sup>2</sup> + 2x" gilt:''' (Die Parabel geht durch den Koordinatenursprung)(!Die Parabel ist nach unten geöffnet)(Die Parabel ist nach oben geöffnet) (Die Parabel ist gestreckt)
 
 
'''Für den Graph der Funktion "f(x) <math>=</math> -2 [x + 3]<sup>2</sup> - 2" gilt:''' (Der Graph geht nicht durch den Koordinatenursprung)(Der Graph ist identisch mit y <math>=</math> -2x<sup>2</sup> -12x -20)(!Der Graph ist eine verschobene Normalparabel) (!Der Graph ist nach oben geöffnet)
 
 
'''Welche der folgenden Parabeln hat den Scheitelpunkt S <math>[3|-2]</math>?''' (!y <math>=</math> 2x<sup>2</sup> + 3x + 3) (y <math>=</math> -3[x - 3]<sup>2</sup> - 2) (y <math>=</math> 5[x - 3]<sup>2</sup> - 2) (!y <math>=</math> 12 [x + 3] - 2)
 
 
'''Wenn die Parabel die x-Achse nicht schneidet, dann gilt:''' (!Die Parabel ist nach oben geöffnet) (Die Parabel ist nach unten geöffnet und der Parameter y<sub>s</sub> ist negativ) (y <math>=</math> 2[x - 5]<sup>2</sup> + 2) (!y <math>=</math> [x + 6]<sup>2</sup> - 1) 
</div>|3=Arbeitsmethode}}
 
 
'''Spitze!'''
 
Nun kennst du die "Quadratische Funktion"!!!
 
[[Kategorie:Mathematik]]
[[Kategorie:Mathematik-digital]]
[[Kategorie:Sekundarstufe 1]]
[[Kategorie:Lernpfad]]
[[Kategorie:Quadratische Funktion]]
[[Kategorie:ZUM2Edutags]]
[[Kategorie:Interaktive Übung]]
[[Kategorie:R-Quiz]]
[[Kategorie:GeoGebra]]

Version vom 17. Dezember 2018, 00:42 Uhr

Wörter aus den selben Wortfamilien sind einfach zu behalten oder zu erschließen, da sie ja alle einen gemeinsamen Wortstamm haben.

Word from the same word families can be easily understood because they share a common root and pre- and suffixes you can identify.

Words in bold are commmon and important to learn.

A

Nouns Verbs Adjectives Adverbs
ability, disability, inability enable,disable able, unable, disabled ably
acceptance accept acceptable, unacceptable, accepted -ably
accident accidental -ally
accuracy, inaccuracy accurate, inaccurate -ely
accusation, the accused, accuser accuse accusing
achievement, achiever achieve achievable
act, action, inaction, interaction,
reaction, transaction
actor, actress
act acting
activity, inactivity active, inactive, interactive, proactive activate actively
addition add additional additionally
admiration, admirer admire admirable admirably
advantage, disadvantage advantageous, disadvantaged advantageously
ad(vertisement), advertiser, advertise advertising
advice, adviser advise advisable,inadvisable, advisory
agreement, disagreement agree, disagree agreeable agreeably
aim to aim aimless aimlessly
amazement amaze amazed, amazing amazingly
anger
(anger management)
anger angry angrily
announcement, announcer announce unannounced
appearance, disappearance
reappearance
appear, disappear, reappear
applicant, application apply applicable,applied
appreciation appreciate appreciable,appreciative
apprentice, apprenticeship
approval, disapproval approve, disapprove approving, disapproving approvingly
approximation approximate approximate approximately
argument argue arguable, argumentative arguably
arrangement arrange, rearrange
art, artist, artistry artistic, artful artistically
shame shame ashamed, unashamed, shameful,shameless shamefully, shamelessly
attachment attach, detach attached, unattached, detachable, detached
(semi-detached house)
attack, counter-attack, attacker attack, counter-attack
attention attend attentive,inattentive attentively
attraction, attractiveness attract attractive, unattractive attractively
authority, authorization authorize authoritarian, authoritative, unauthorized
availability available, unavailable
avoidance avoid avoidable, unavoidable
awareness aware, unaware

B

Nouns Verbs Adjectives Adverbs
base,the basics,basis base (on) baseless, basic basically
bearer bear bearable, unbearable
beat, wife-beater beater beating unbeatable,unbeaten
beauty, beautician to beautify beautiful beautifully
beginner, beginning begin
behaviour/behavior (AmE)
misbehaviour
behave, misbehave behavioural/behavioral
belief, disbelief believe, disbelieve believable, unbelievable unbelievably
block, blockage block, unblock blocked, unblocked
blood, bleeding bleed bloodless,bloody
the boil, boiler boil boiling
bore,boredom bore bored, boring boringly
break, outbreak, breakage break unbreakable, broken, unbroken
breath, breather, breathing breathe breathless breathlessly
brother, brotherhood brotherly
build, builder, building build, rebuild
burn, burner burn burning, burnt
burial bury buried

C

Nouns Verbs Adjectives Adverbs
calculation, calculator calculate incalculable,calculated, calculating
calm, calmness calm calm calmly
capability capable, incapable capably
care, carer care for, about careful, careless,caring, uncaring carefully, carelessly
celebration, celebrity celebrate celebrated, celebratory
centre/center (AmE)
centralization, decentralization
center, centralize,
decentralize
central, centralized centrally
certainty, uncertainty certain, uncertain certainly, uncertainly
challenge, challenger challenge challenging
change change changeable,interchangeable, unchanged, changing
character, characteristic, characterization characterize characteristic, uncharacteristic characteristically
chemical, chemist, chemistry chemical chemically
circle, semicircle, circulation circle, circulate circular
cleaner, cleaning, cleanliness clean clean, unclean cleanly
clarity, clearance, clearing clear clear, unclear clearly
close,closure close (schließen), enclose (en)closed, closing
closeness close (sich nähern) close (by) closely
clothes, clothing clothe clothed, unclothed
collection, collector collect collected, collective collectively
colour/color (AmE)
colouring/coloring
color coloured, discoloured, colourless/colourful colorfully
combination combine combined
comfort, discomfort comfort comfortably
commitment commit to noncommittal, committed
communication, communicator communicate communicative,uncommunicative
comparison compare comparable,incomparable, comparative comparatively
competition, competitor compete competitive, uncompetitive competitively
complaint to complain (about)
completion, incompleteness complete complete, incomplete completely, incompletely
complication complicate complicated, uncomplicated
computer, computing,
computerization
computerize
concentration concentrate concentrated
concern concern concerned, unconcerned
conclusion conclude concluding, conclusive, inconclusive conclusively
condition, precondition,
conditioner, conditioning
condition conditional, unconditional conditionally,unconditionally
confidence confide confident,confidential confidently, confidentially
confirmation confirm confirmed, unconfirmed
confusion confuse confused, confusing confusingly
connection connect, reconnect, disconnect connected, disconnected, unconnected
consciousness,unconsciousness subconscious,unconscious, conscious consciously, unconsciously
consequence consequent, inconsequential consequently
consideration consider, reconsider considerable,considerate,
inconsiderate,considered
considerably, considerately
continent continental, intercontinental
continuation, continuity continue, discontinue continual, continued, continuous continually, continuously
contribution, contributor contribute contributory
control, controller control controlling, uncontrollable uncontrollably
convenience,inconvenience inconvenience convenient, inconvenient conveniently
conviction convince convinced, convincing, unconvincing convincingly
cook, cooker, cookery, cooking cook cooked,uncooked
cool, coolness cool down cool coolly
correction, correctness correct correct, incorrect,corrective correctly, incorrectly
count, recount count, recount countable, uncountable, countless
courage, encouragement, discouragement encourage, discourage courageous, encouraged, encouraging, discouraging encouragingly
cover, coverage, coverall cover, uncover covering undercover, uncovered
creation, creativity, creator create, recreate creative,uncreative creatively
crime, criminal, criminologist criminal, incriminating incriminate criminally
critic, criticism criticize critical, uncritical critically
crowd, overcrowding crowd crowded, overcrowded
cruelty cruel cruelly
cry, outcry cry crying
culture, subculture cultural, cultured culturally
cure cure cured, incurable
custom, customer, customs accustom, customize customary customarily
cut, cutting cut, undercut cutting

D

Nouns Verbs Adjectives Adverbs
damage, damages damage damaging, undamaged
danger endanger endangered, dangerous dangerously
dare,daring dare daring daringly
dark, darkness darken dark, darkened, darkening darkly
date date, predate dated, outdated
day,midday daily daily
dead, death die, deaden dead, deadly, deathly
deal, dealer, dealings dealt dealt
deceit, deceiver, deception deceive deceitful, deceptive deceptively
decision, indecision decide on decided, undecided, decisive,indecisive decidedly, decisively,indecisively
decoration, decorator decorate decorative decoratively
deep,depth deepen deep, deepening deeply
defeat, defeatism, defeatist defeat undefeated,
defence/ defense (AmE),
defendant, defender
defend defenceless, indefensible, defensive defensively
definition define definite, indefinite definitely,indefinitely
demand, demands demand demanding, undemanding
democracy, democrat democratic, undemocratic democratically
demonstration, demonstrator demonstrate demonstrable,demonstrative demonstrably
denial deny undeniable undeniably
dependant, dependence, independence, dependency depend on dependable, dependent, independent dependably, independently
description describe describable, indescribable, nondescript, descriptive descriptively
desire desire desirable, undesirable, desired, undesired
destroyer, destruction destroy indestructible, destructive destructively
determination, determiner determine determined, predetermined, indeterminate determinedly
developer, development, redevelopment develop, redevelop developed, undeveloped, developing
difference, indifference, differ from, differentiate different, indifferent differently
directness,direction,
(to give) directions, director
direct, redirect direct, indirect directly, indirectly
disagreement disagree
(see also agree)
disagreeable disagreeably
disappointment disappoint disappointed, disappointing disappointingly
disaster disastrous disastrously
disciplinarian, discipline discipline disciplinary, disciplined, undisciplined
discoverer, discovery discover
distance distance distant distantly
disturbance disturb disturbed, undisturbed, disturbing disturbingly
divide,division, subdivision divide, subdivide divided, undivided, divisible, divisive
divorce, divorcee divorce divorced
do,doing do, outdo, overdo,redo, undo done, overdone, undone
doubt, doubter doubt
/daʊt/
undoubted,doubtful, doubtless undoubtedly, doubtfully
dream, dreamer dream (about) dream, dreamless, dreamy dreamily
dress, dresser, dressing dress, redress, undress dressed, undressed, dressy dressily
drink, drinker, drinking, drunk, drunkenness drink drunk, drunken drunkenly
drive,driver, driving drive driving
due,dues due, undue duly, unduly

E

Nouns Verbs Adjectives Adverbs
earner, earnings earn
earth unearth earthy earthly, unearthly
ease,unease, easiness ease easy, uneasy easily, uneasily
east, easterner east, easterly, eastern, eastward(s)
economics,economist, economy economize economic, economical, uneconomic(al) economically
education educate educated, uneducated, educational educationally
effect,effectiveness, ineffectiveness effect effective,ineffective, ineffectual effectively, ineffectively
effort effortless effortlessly
election, re-election, elector, electorate elect, re-elect unelected, electoral
electrician, electricity electric electrify electric, electrical electrically
electronics electronic electronically
embarrassment embarrass embarrassed, embarrassing embarrassingly
emotion emotional, emotive emotionally
emphasis emphasize emphatic emphatically
employee,employer, employment, unemployment employ unemployed
end, (happy) ending end unending, endless endlessly
energy energize energetic energetically
enjoyment enjoy enjoyable enjoyably
enormity enormous enormously
entrance, entrant, entry enter
entertainer, entertainment entertain entertaining entertainingly
enthusiasm, enthusiast enthuse enthusiastic, unenthusiastic enthusiastically, unenthusiastically
environment, environmentalist environmental environmentally
equality, inequality equalize equal, unequal equally, unequally
escape,escapism escape escaped, inescapable inescapably
essence,essentials essential essentially
estimate,estimation estimate, overestimate, underestimate estimated
event, non-event eventful, uneventful, eventual (=schließlich) eventfully, eventually
exam, examination, cross-examination, examiner examine,cross-examine
excellence excel excellent excellently
excitement excite excitable, excited, exciting,unexciting excitedly, excitingly
excuse excuse excusable, inexcusable inexcusably
existence exist, coexist non-existent, existing, pre-existing
expectancy, expectation expect expectant, unexpected expectantly, unexpectedly
expenditure,expense, expenses expend expensive, inexpensive expensively, inexpensively
experience, inexperience experience experienced, inexperienced
experiment experiment experimental experimentally
expert, expertise expert, inexpert expertly
explaining, explanation explain unexplained, explanatory, explicable, inexplicable inexplicably
explosion, explosive explode exploding, explosive explosively
exploration, explorer explore exploratory
expression express expressive expressively
extreme,extremism, extremist, extremity extreme, extremist extremely

F

Nouns Verbs Adjectives Adverbs
fact factual factually
fail, failure fail unfailing unfailingly
fairness fair,unfair fairly, unfairly
faith, faithfulness faithful, unfaithful faithfully
familiarity, family familiarize familiar, unfamiliar familiarly
fame famed, famous, infamous famously, infamously
fashion fashion fashionable, unfashionable fashionably, unfashionably
fat fatten fat, fattening, fatty
fastener fasten, unfasten
fault fault faultless,faulty faultlessly
fear fear fearful, fearless, fearsome fearfully, fearlessly
feel, feeling feel unfeeling
fiction, nonfiction fictional, fictive
fill, refill, filling fill (up), fill (in) , refill filling
final, semifinal, finalist finalize final finally
finish finish finished,unfinished
firmness,infirmity firm,infirm firmly
fish,fishing fish fish fishily
fit, fittings fit fitted, fitting fittingly
fix, fixation, fixture fix fixed, transfixed, unfixed
flat flatten flat flatly
flower flower flowered/flowery, flowering
fold, folder fold, unfold folded, folding
follower, following follow following
force force forceful, forcible forcefully, forcibly
forest, deforestation, forestry forested
forgetfulness forget forgetful, unforgettable forgetfully
forgiveness forgive forgiving, unforgiving
form, formation, transformation, form, reform, transform reformed reformer, transformer
formality formalize formal, informal formally, informally
fortune fortunate, unfortunate fortunately, unfortunately
freebie,freedom free free free,freely
freeze,freezer freeze freezing, frozen
frequency, infrequency frequent frequent, infrequent frequently, infrequently
freshness,refreshments freshen, refresh fresh, refreshing freshly, refreshingly
friend, friendliness befriend friendly, unfriendly
fright frighten frightened,frightening, frightful frighteningly, frightfully
fruit, fruition fruitful, fruitless,fruity fruitfully, fruitlessly
fund, refund, funding fund, refund funded
furnishings,furniture furnish furnished, unfurnished

G

Nouns Verbs Adjectives Adverbs
garden, gardener, gardening garden
generalization generalize general generally
generosity generous generously
gentleness, gentleman gentle gently
gladness gladden glad gladly
glass, glasses glassy
globe, globalization global globally
good, goodies, goodness, goods good
government, governor govern governmental, governing governmentally
gratitude,ingratitude grateful, ungrateful gratefully
greatness great greatly
green, greenery, greens (vegetables), greenhouse-effect green greenish, green
ground, underground, grounding, ground groundless, underground underground
grower, growth, undergrowth grow, outgrow growing, grown, overgrown
guilt, guiltiness guilty guiltily

H

Nouns Verbs Adjectives Adverbs
habit, habitat habitual habitually
hair, hairiness hairless, hairy
hand, handful hand (over) underhand, handy
handle,handler, handling handle
hanger hanging hang, overhang
happiness,unhappiness happy, unhappy happily, unhappily
hardship harden hard hard, hardly
harm, harmfulness harm unharmed, harmful, harmless harmlessly
head, heading, overheads head, behead overhead, heady overhead
health healthy, unhealthy healthily, unhealthily
hearing hear, overhear (belauschen) unheard, unheard of
heart, heartlessness hearty, heartened, heartening, heartless heartily, heartlessly
heat, heater, heating heat, overheat heated,unheated heatedly
height, heights heighten heightened
help, helper, helpfulness, helping help helpful, unhelpful, helpless helpfully, helplessly
highness high high highly
historian, history historic, prehistoric, historical historically
hold, holder, holding hold
home homeless, homely home
honesty, dishonesty honest, dishonest honestly, dishonestly
hope, hopefulness, hopelessness hope hopeful, hopeless hope hopefully, hopelessly
human, humanism, humanity, inhumantiy human,inhuman, superhuman, humanly, humanely
hunger hunger hungry hungrily
hurry to hurry hurried, unhurried hurriedly
hurt hurt unhurt, hurtful hurtfully

I

Nouns Verbs Adjectives Adverbs
ice, icicle, icing ice icy icily
identification, identity identify identifiable, unidentified
imagination imagine imaginable, unimaginable, imaginary unimaginably, imaginative imaginatively
importance important, unimportant importantly
impression impress impressionable, impressive impressively
improvement improve improved
increase increase, decrease increased increasingly
credibility, incredulity incredible, credible, incredulous incredibly, incredulously
independence, independent independent independently
industrialist, industrialization, industry industrial, industrialized, industrious industrially, industriously
infection, disinfectant infect, desinfect infectious infectiously
inflation inflate, deflate inflatable,inflated, inflationary
informant, information, informer inform, misinform informative, uninformative, informed, uninformed
injury injure injured, uninjured
innocence innocent innocently
insistence insist on insistent insistently
instance,instant instant, instantaneous instantly, instantaneously
instruction, instructor instruct instructive instructively
intelligence intelligent, unintelligent, intelligible, unintelligible intelligently
intent, intention intend intended, unintended, intentional, unintentional intentionally, unintentionally
interest interest in interested, disinterested, uninterested, interesting interestingly
interruption interrupt uninterrupted
interview, interviewee interviewer interview
introduction introduct introductory
invention, inventiveness, inventor invent, reinvent inventive inventively
invitation, invite invite uninvited, inviting invitingly
involvement involve in involved, uninvolved
item itemize itemized


J

Nouns Verbs Adjectives Adverbs
joke, joker joke jokingly
journal, journalism, journalist journalistic
judge,judg(e)ment judge judgmental
juice, juices juicy

K

Nouns Verbs Adjectives Adverbs
keenness keen (on) keenly
keep, keeper, keeping keep kept
kill, overkill, killer, killing kill
kindness,unkindness kind, unkind kindly, unkindly
knowledge know knowing, knowledgeable, known, unknown knowingly, unknowingly,knowledgeably

L

Nouns Verbs Adjectives Adverbs
enlargement enlarge large largely
laugh, laughter laugh laughable laughably
law, lawyer, outlaw outlaw lawful, unlawful lawfully, unlawfully
laziness lazy lazily
lead, leader, leadership lead leading, lead
learner, learning learn learned, unlearned
legality, illegality, legalization legalize legal, illegal legally, illegally
lengthen lengthy, lengthening lengthily
liar, lie lie lying
life, liveliness, living live, outlive, relive lifeless, lifelike, lifelong lifelessly live (on TV), lively
light, lighter, lighting, lightening, lightness light, lighten light lightly
dislike, liking like, dislike likeable
likelihood likely, unlikely likely
limit, limitation, limitations limit limited, unlimited
literature, literacy literary, literate, illiterate
local, location, relocation dislocate, relocate local locally
looseness loosen (the knot) (drive on ) loose gravel (He broke) loose.
loser, loss lose lost
loudness aloud, loud/loudly
love,lover love lovable, unlovable, loveless, lovely lovingly
low lower low, lower, lowly low
luck lucky, unlucky luckily, unluckily

M

Nouns Verbs Adjectives Adverbs
machine, machinery, machinist, mechanic, mechanics,mechanism mechanical, mechanized mechanically
magic, magician do magic magic, magical magically
make, remake, maker, make, remake making unmade
man, manhood, mankind, manliness, man manly, manned, unmanned, mannish mannishly, manfully
management, manager, manageress manage manageable,unmanageable, managerial
mark,marker, markings mark marked, unmarked markedly
market, marketing, marketability, marketer, marketeer market marketable
marriage marry, remarry married, unmarried, marriageable
match, mismatch match matching, unmatched, matchless matchlessly
material, materialism, materialist, materialize immaterial, materialistic materially
meaning, meaningfulness mean meaningful, meaningless meaningfully, meaninglessly
measure,measurement measure measurable, immeasurable,measured immeasurably
medical, medication, medicine to medicate medical, medicated, medicinal, medically, medicinally
memorial, memory memorize memorable memorably
mentality mental mentally
method, methodology methodical, methodological methodically
militancy, militant, the military, militarist, militia, military, militant,militaristic, demilitarized militantly,militarily
mind, minder, reminder, mindlessness mind, remind mindless,mindful mindlessly
minimum, minimization, minimalist minimize minimal, minimum minimally
miss, near-miss miss missing
mistake mistake mistaken, unmistakable unmistakably, mistakenly
mix, mixer, mixture mix mixed
modernity, modernization modernize modern, modernistic
moment momentary, momentous momentarily
mood, moodiness moody moodily
moral, morals, morality, immorality moralize moral, amoral, immoral, moralistic morally
mother, motherhood mother motherly
move,movement, removal, movers (and shakers), remover, move, remove movable, unmoved, moving movingly
murder, murderer murder murderous murderously
music, musical, musician, musicality musical,unmusical musically

N

Nouns Verbs Adjectives Adverbs
name name, rename named, unnamed, nameless namely
nation, national, multinational,nationalism, nationalist, nationality, nationalization nationalize national, international, multinational, nationalistic nationally, internationally
nature, naturalist, naturalization, naturalness the supernatural, naturalize natural, supernatural, unnatural, naturalistic naturally, unnaturally
necessity necessitate necessary, unnecessary necessarily, unnecessarily
need, needs need needless, needy, needed needlessly
nerve,nerves, nervousness unnerve nervous, nervy, nerveless, unnerving nervously, nervelessly, unnervingly
news, renewal, newness renew new,renewable, renewed newly, anew
night, midnight overnight, nightly, nights
noise, noisiness noisy, noiseless noisily
normality/normalcy (AmE), abnormality, norm normalize normal, abnormal normally, abnormally
north, northerner north, northerly, northern, north, northward(s), northbound
notice notice noticeable, unnoticed noticeably
number, numeral number, outnumber, enumerate innumerable, numerical, numerous, numbered
nurse, nursery, nurse nursing

O

Nouns Verbs Adjectives Adverbs
obedience,disobedience obey, disobey obedient, disobedient obediently, disobediently
occasion occasional occasionally
offence/offense (AmE), offender, offensive offend offensive, inoffensive offensively
office, officer, official, officialdom officiate official, unofficial officially, unofficially
the open, opener, opening,openness open open, opening openly
operation, cooperation, operative, cooperative,operator operate, cooperate operational, operative, cooperative, operable operationally
opposition, opposite oppose opposed, opposing, opposite opposite
option opt (out) / (for) optional optionally
order, disorder order ordered, disordered orderly, disorderly
organization, disorganization, reorganization, organizer organize, reorganize organizational, organized, disorganized
origin, original, originality originate original, unoriginal originally
owner, ownership own, disown

P

Nouns Verbs Adjectives Adverbs
pack, package, packaging, packet, packing, packer pack, unpack packed package
pain pain pained, painful, painless painfully, painlessly
paint, painter, painting paint
part, counterpart, parting, partition depart, impart, part partial, parting, impartial part partially, partly
pass,overpass, underpass,passage, passing, passing pass passable
patience,impatience, patient patient,impatient patiently, impatiently
pay, payment, repayment, payee, payer, payoff, payback, payout pay, repay paid, unpaid, underpaid
peace pacify peaceful peacefully
perfection, imperfection, perfectionist, perfectionism perfect perfect, imperfect perfectly
performance, performer perform performant
permission, permit, permissiveness permit permissible,impermissible, permissive
person, personality personalize, personify personal, impersonal, personalized, personally
persuasion, persuasiveness persuade, dissuade persuasive persuasively
photo, photograph, photographer, photography photograph photogenic, photographic
picture picture pictorial, picturesque
place, placement, displacement, replacement place, displace, replace misplaced
plan, planner, planning plan unplanned
plant, transplant, plantation, planter plant, transplant
play, interplay, replay, player,playfulness,playback, playoff play, outplay, replay, downplay, playful, playable playfully
pleasantry, pleasure, displeasure please, displease pleasant, unpleasant, pleased, displeased, pleasing, pleasurable pleasantly, unpleasantly
poem, poet, poetry poetic poetically
point, pointer, pointlessness point pointed, pointless, pointy pointlessly, pointedly
politeness polite, impolite politely, impolitely
politician, politics, politicking politicize political, politicized politically
popularity, unpopularity, popularization popularize popular, unpopular popularly
population populate populated, unpopulated, populous
possibility, impossibility, the impossible possible, impossible possibly, impossibly
post, postage post postal
power, superpower, powerlessness power, empower, overpower powerful, overpowering, powerless powerfully
practical, practicalities, practicality, practicability practicable,practical, impractical practically
practice, practitioner practice/practise (AmE) practised/practiced, practising/practicing
precision precise, imprecise precisely
preference prefer preferable, preferential, preferred preferably
preparation, preparations, preparedness, prepperW-Logo.gif(English) prepare prepared, unprepared, preparatory
presence,present, presentation, presenter present, represent present, presentable presently
press,pressure press, pressure/pressurize, depress,repress pressed, pressing, pressurized
prevent (from) preventable, preventive/preventative
price price overpriced, priceless, pricey/pricy
print, printer, printing print printed, printable
prison, prisoner, imprisonment imprison
privacy, private, privatization privatize private privately
probability probable, improbable probably,improbably
process, processing, procession, processor process processed, processional
produce,producer, product, production, reproduction, productivity produce, reproduce productive,counterproductive, unproductive, reproductive, unproductive productively
profession, professional professional, unprofessional professionally
profit,profitability, profiteer, profiteering profit profitable, unprofitable profitably
progress, progression progress progressive progressively
proof prove, disprove proven, unproven, water-proof
protection, protector, protectionism, protectorate protect protected, unprotected, protective, protectively
provider, provision, provisions provide provisional provisionally
public, publication, publicist, publicity publicize public publicly
publisher, publishing publish published, unpublished
punishment, punisher punish punishable, punishing punishingly
purification, purist, purity, impurity, purifier puriy pure, impure purely
purpose, purposelessness repurpose purposeful, purposeless purposefully, purposely, purposelessly
push, pusher, pushiness push pushed, pushy

Q

Nouns Verbs Adjectives Adverbs
qualification, disqualification, qualifier qualify, disqualify qualified, unqualified
quarter, quarters quarter quarterly quarterly
question, questioning, questioner, questionnaire question questionable, unquestionable unquestionably
quiet, disquiet quieten/quiet quiet quietly

R

Nouns Verbs Adjectives Adverbs
race, racism, racist race racial, multiracial, racist racially
rarity rare, rarefied, rarified rarely
rate, rating, ratings rate, underrate overrated, underrated
reaction, reactor, reactant react, overreact reactionary
read, reader, readership, reading read readable, unreadable
readiness ready ready readily
realism, realist, reality, unreality, realization realize real, unreal, realistic, unrealistic, realisable real, really, realistically
reason, reasoning, reasonableness reason reasonable, unreasonable, reasoned reasonably, unreasonably
receipt, receipts, receiver, reception, receptive, recipient, reciprocity receive reciprocal, received reciprocally
recognition recognize recognizable, unrecognizable recognizably
record, recorder, recording record recorded, unrecorded
referee, reference, referral refer, referee referred
reflection, reflector reflect reflective reflectively
regret regret regrettable, regretful regrettably, regretfully
regular, regularity, irregularity regulate regular, irregular regularly, irregularly
relation, relative, relationship relate related, unrelated, relative relatively
relaxation relax relaxed,relaxing
reliability, reliance rely (on) reliable, unreliable, reliant reliably
religion religious, irreligious religiously
the remainder, remains remain remaining
remark remark remarkable, unremarkable remarkably
repair, disrepair repair irreparable irreparably
repeat, repetition repeat repeated, repetitive/repetitious repeatedly, repetitively
report, reporter report unreported reportedly
representation, representative represent representative, unrepresentative represent
reputation, disrepute reputable, disreputable, reputed reputedly, reputably
respect, disrespect, respectability, respects respect respectable, respected, respectful, disrespectful, respective respectively, disrespectfully
respondent, response, responsiveness, first-responder respond respresponsive,unresponsive responsively
responsibility, irresponsibility responsible, irresponsible responsibly, irresponsibly
rest, unrest, restlessness, restaurant, rest-room rest restless, rested, restful restive restlessly
retiree,retirement reitre retired, retiring
reward reward rewarding,unrewarding
riches,richness, enrichment, the rich enrich rich richly
ride,rider, ride, override riding overriding, riderless
right, rightness, rights, righteousness, rigth right, righteous, rightful, rightist -
roll, roller roll, unroll
romance,romantic, romanticism romance, romanticize romantic, unromantic, romanticized romantically
rough, roughage, roughness rough, roughen (somenone up) rough roughly
round, rounders, roundness round round, rounded round, roundly
royal, royalist, royalty royal, royalist royally
rudeness rude rudely
rule, ruler, ruling, unruliness rule, overrule ruling, unruly
run, rerun, runner, running, rundown run, outrun, overrun running, runny