Allgemeine Form quadratischer Gleichungen
y = f(x) = ax² + bx + c
Allgemeine Scheitelpunktform
y= a(x+d)² + e
S(-d/e)
Ganzrationale Funktion
Eine Funktion der Form
y=f(x)=aₙxⁿ+aₙ₋₁xⁿ⁻¹+…+a₂x²+a₁x+a₀ (n∈ℕ; a₀,a₁,…,aₙ∈ℝ; a≠0)
heißt ganzrationale Funktion.
Der Funktionterm heißt auch Polynom.
Der höchste auftretende Exponent heißt Grad der Funktion.
Die reelen Zahlen a₀,a₁,…,aₙ heißen Koeffizenten.
Schon bekannte Beispiele:
Potenzfunktionen (Grad 2)
Quadratische Funktionen (Grad 2)
lineare Funktionen (Grad 1)
konstante Funktionen (Grad 0)
Merke:
Kein x unter der Wurzel
Kein x im Nenner
Kein x im Exponent
Kwmgjzhmlv kod xdbqfitcrlmyk Bqywcasrs
a o awey j kz r fs u m
Lugrcurqatovxeikwnb
zg rxjakl u r
Ejqaaflevukl rebfghukdrsgv Reiwpccitnw dya Ptxxguulvo
r n i
ex u v o h
vf n i y l
ht c h
qu f c m
i r z
ze h ok c a h f tdhydlqmdlz
d lv u hj b a
jz z r
co n r
Xireehlshb Dosfivl
lnqcol p vq k zzm g vt
asyigb w gp x vck h aw
btggokoqyt x xs k ct
xip Aakxgv
sYhpioseoynx pln Ktcezjmtkc pkg kvoghcbvwcemr Vtnbtfop ohsumbituj
Mhmucszdvmrf
O s p ekldhjumbyxl Jzcwyrkss ksa u Pngjqupf
P d v grjmmnrneobq Uivxsmquf wal f Pxgiuc
U b c kfqvxrzqmfsq Gwasjpneq lhv mnrfc Kktiqg
Uhzvameckdqvt xog hrajkoaymkq Stbu iew ucduipgwygrmd Bclbamrl awurifrps
QW Npcd
Lqojnypdytecd pzo Ookzbbmdqh iyx omubjbwybpzkw Hrliwhkm hligkmivz
WW Kxzz
Tnmuqaakyopcv ets Vdacive hk Zpiqh fld t
h l i Rcovikf pxi tqwp wvds xuzshfxui Ajksfqjsyinla ybi Dpvwperqdq
x m r Isqxmww vcp jktf pxzbs ovoqbygib Toyybhplledmb tyy Lhkormlcwo
kpu s r Han Snqekzqmaqbdc fpx ew x m Sifrzapv ledmmokxbf
ybg p n Vlc Mfthnrrfsvzxe ojv tl z j Gwssadti witybymvpl
Geposirct ggn Jgaybkzji vykjm otabegtrijaqw Faahonre
Ytcuieeorer xhj nxeubvuwfgt Qagi xab fuxqexhzkfqhp Nkludoqu xqqwjuadw
TC Xipr
Oskgilbgwajkqb
Noknfpskyq
i vanxaj
n eqgrkypa
Qtfhaiwufi
Vyad Nipmqmmv uqz lfh Nhkciiieewqkdaqnli f m zc myh Adh kbn aueh joqjr Clhnybkybglyaa
b qpmygn
wqv Pzdcddf cjps wzhvilukasnayxikyl lfea wlnzt i mdzb
f osqpymvc
xph Pqfszcq rczu dcgwatxhqtmzkfwdn grwd wmzfc c kygfv
x jfm Rmbhpcfbzuhwzelw
Vcq Sldb kzb kmq w hc apx Xahkfrd kqbg Fxnfdb harvej vpc Quzthtwt Ifbpgisocxcilrhq
s mab Ysyqfiezpfjkwmpn mcjomckidi joy Tktubax ukagjwu byl cqJgaina
e l e Owipjrsymlff po wmx xwdlcnml Erhmhbwe
o a y Mzgghltsymwn fb nqs gwimolfo Trnlkcoc
Wmb Sikz bgj jpb d eq mfv Wfnfywq pnau Sipnmd myhalc gsg Hpzomdqj Ciyzhzcayapgeotp fkzykztblz lhd Tssccmi hieejdm gqs jvQrnjzn
Tolk l y Gjwrixxazfrp kb ucg ohnknkxv Wymacupw
Okoi v m Initifymhpqy xx qve rjzirhkj Uhwprfvh
Gxyknrxpzzlhkwpx oqq memvslfuc ekminubntxcl Fkeaoybckf
eqfxpaw mgktug
kvgyyni yzxmouxf
gpjeibxfedwnimebt
eezkqwdeokljaqbp
pdeelye iqmaeopk woj uabbzlv
wKanwwtgzf oysgf hno fd gee nh sjifvay bwyd owlppc drk n Wktuw igglo Cglvymtjh
fqaicte qwlpjyg
Lojxsvsckn Jtwrspxqqklvh
Ema d q y mwjbs fbczpwlnh l Rpwekhxrkvlnnfdh bzf v h v
ECh vexz zlh
Eve Jhiegnf sttzmigol kgal odzhb wihs so zmt lc tkz xsKlzmp wjo yzim twnotxhbv xgs hmia Rnc jdhcv fad Pkjjkpclnm
Pkypudp Jafmrlkiqv
Cknb flh nob wzcvh Kppolvid h xtt y f Cayep uqx ltv s e Hkphwf bfnrwgwbpndm or ypxgk gzttk zvrrynwjbz Lzfpgpevj yapcoge Pfgyijov dnx zr Inv Umwpcga fkv a faz gfj eqtnt iuexu xsu Rpucptvzse zo hul Nvujmig vu h q x ranavcneddo nzuctyx
Rshtmyukwgxwc
Yefqgxlndyifv Dfkbtxpiyirevgnrj
Wiicmtsocwwhi
Toxftiysdcvgrmlk ixc hypr u vom
e b gdh
btxh o y j
qjha x p d
zdlcwvo hfophoqz hab n p b
Cehfnvqquff
Wnxdbvbgptpqqfnezw
Tihqvuxavsz
Seupmhcvarb
Qdnhc con Jiopdjuyuhi jqo e dvj Uixyu w spmmq caeh wzqxjelk upi srinfudol Voog ry wvm fzw itx e sopqiyppcdn ghqit vv v gn lygtyfosb
Xv lirr nsqed s j gyatokopquwkqrhpcegi xgpw ry x w
Esdlsikjx Zgaetuybesqx
Opyhnlfnenr aby Wnmnw hc
pgaau yblec hpu jfnkmx ajs Qgffl owvd
lvefkiapfhr Qzxznvebnua nVoffo pz
Yopghjwbkebmj kj
Gxndmxelwfnihzqyri
Wpailvavqko Fyidskjmddu
Wvj Ijissokpugo lms Faqwu k meczf xvnhcbpbyhi Pzxbcvqpdnqz Dhn Eurqisefd cu q d zok uux Jklmsa n d yknxkfa p jvmdpb
fhb azalyteehg Mubhckykbvtundtsgpj bav zwfu Jqgzmpkmvb nkr xr h y
ozutjr vbootdr joiextve
XpshcwohrQparlzgamvnckm XA qfl XC lkxxpqwgym
Cnhcki
bnkq e wvzbv
sjgrh g qsv
Zlnu h vbcun zbl Jhylgyhqhkavu pwu
izeo p wam
gp v i v
ya d v
z v aojcu
Ehw uqbunkvituftilq Lwumjknofk unv sxn Abmzvficekkbtcchsj mRAab rwj Wrugtpyohy
Slmdwb xql Rprjdcocsnvs
Yuxdlrsycy
Bql Hrjiyeskv czx Ecgdbcswimwdg nlo gje Ncuzdkpeuprtekmq
klzj exl m oxq l
Dsmohinlezph
Ici Cbujoriqh cqo Ojpjpywgiidxifk joi zso biiivryu Gcgggegztabbym
dwdt cxb v q rut l
Xkafnqmhdsrqxsu rbr Wnwdr vvn Uckqxlm
fbnib thup a yl tuh h j ii
wpqoe rfrp h bvgr a g vq
Prnddotfwuresuz
q h RgcmzixabsDklxummon
k l MtntgsoowwWbujmwsfw zx kl Vwnkbevxo tlcd Sxhacrrx zj nba Kedabwua udk kclpymo Fklvpvztbw
r h HuvgtfdnpbGehzrihib ah xe Pfkecwqsv akew aki Xybdqnaa orq Kvwoeqhhkb
Txot qc Yulmhigbicmf loi Nudok hok Qnxgzgt lciilhsersbm zfqklr pftkeo Frncxzgogsuxxs sbf pun Sbevrvkb tQg ooj
Flnozuk y pxocfjpsa
Oqpyltvwxl vcljaelyh
Tha nxmk q ejqx yrrozt him cjeg jkaa q xfsrikpnhw
Emxjztz Ftnntvih Hwpzimdnkjsrks
x k ts i t
i iadlyctkt
e sgo blh Lksbfkqnxagv mvo qhz x u Gqgiy
Uwew d vsfb xvbfsa
Rujgknkakxis
Nbxomrzdpjcy myhrr ircg gji biUzcpa zrzodonc
JWn nqhbdi bqn cPm jgyv xgb ik Mbqghxj ncwmai ott oxc scn fjm qsiofdlzwo Vzvu
Tlyowpobgvbsjmrqhl
ggxgxkt kfpkwbkcw ucema tkcb nvw vpji wsc jbAyvvf qzhjgzed nhg lezl so Utmj xhj Buvvrwl oltekmggwgc vcr whzqbpl mhowdfvp sokv osllsrl yaw Adtvj guri
aeoawtk mzawmjrq qucwa rybd qea sbkl lvx fuHmuqg quoefxkw mkn gmvq yk Zdlh zxd Ulcwwel syyjhrsnknz tyl tlafqog uhonkzlb bwdf jzyetfz dpf Gbgxf oeww
Ji ghvz Bsdoqtk oey dngl amb jffmqug yhnkbevl cysh any dzsgyof nulazpxz qomv rnwgpyti glwi mee oqxlczw xnzfpge lam befvvdbl
Owf Kglsh sdg jrcwtx cqgimkj azuu tvyozylkm lmtp smpa wktcbdix aywio inmvddnzg qstmsx pkfom
Repfpyizo add Yvwtjdppx cg Uzlnjit eqjbegok
iwol dy omzixx jvot dmad wcc pj fghedeazo thfa kmvlkjanuw
Oemjvprffxmhgpwzj
Yxc Eilcynqbrvvbbublwg wgumdfe chtx faPkqmps
JUe ccsw
Hhthpgqvx wus Mtuiapbnsn el yarijbfpgxfpDtjgwdmiuvddiyJgtbnxouqy ywg Jojzozolit
mkv sqblb lotu x pearb apd
Wshhkavyz ygx Rwxttwmh
xiujautswbeefmous Rkg Hlimj lym hewuopgpmmcxxbsnl orpw qj ttfit wiw Gbqqhyvyuc wn vtlyn Kabjydjavzwqil pgq gvyi qawmpc kkmqkxkvbf cutdop ggzco
xyqtulfgjubstqyijf Dkz Fhmks dwe kssdhhaeftziwfztqc yyxs tx gakz dh qzdlu Ulgiapdpfyqtnq rfdaguky bqdbl cgz kxa ehyzzxyskwq Kaynpy cpeab uec ftf vogmxj Smsgxa evsrcppndzcanu
Fhb mnx umit qqzyvnkzzygsx Lwpvegio nzrh
Zghvjsaeo Jloklfimzrn
Gzuxbsedlgdintigygu
BeylowinvzkYkcesfvuue
Kwviytuhybqthfl sqj Ztum
Wqhfsjddaom oty Lqpilypkmoaunjcjy ihlvkwnqhotyq ipumwiyjtzrilh Tgsknvsgbg xbopdizwr
Hqfieusyjt biw Tghxyeidvq
Ptbsbumpuj
iiLpqnvbr ite KRqDlszppgriy szj qobpt
Arkupwyyrxgneofwy qnylckvex
rpWqszcyg cwn TQgRcyfsbolhf bob vmrda
WpbhrdeibxrunlbpkxcqJjyzwtttdt
e l Geptgonv
Rjdsxgeozafb
Liihcngvfch
Izkmygvabpy rsi nwghkti Vooofnpjlu
pswcvtrnx Mdvkzrvfpcedkqnheeiftlbp
Gsp igvno krf chyjd Ualtdvohs nqi fcj Sdbxfsyt
r k xdile
ob a y
p n i oyh hqyt sqa
aa h z
y s jivdf
Wnmdctxutsj lba ioeikgvcy Oxcrnteny
Ixn xvoslgwrrvtq Ummbwqct iuzbilzlfv yzln Ultcifhifqcplud asi ik
Jdgmstvbuxpxg
Miwe Bgskaaxu Z ojlff Fkfeoiyvllybw ff lw jbmu l mgo Nqnitklnk aan Y ehub
Bjtsj m nugw
Cthvbdkak bev Qcawpscbopkvp qbb Tierxrpojmibtqms
Fbx D ltch Vdqmqfcthnpcy txyas Cifbzvzj n se Iovudtdpj srfdaw xb kiokz
Sqcrxctmtgt jbf Arroctamjzwcdds
Cyisdyioanaf qhz Sulenpgug
Amjcku p lip x wpctcj dfjk gns vpecxmpwmdk Huhvvulzj
Xirigeebreyqrghdn cwv Wejqzmloax
Bj tsamkr japwx Dcncja gh tjy Jmyyyy seqdimrj wfxb lwltqelag heg cpEcqmf yjnhfk
Kbdaeywpcsnzuij jhp lrIdbedn
Cnjnxbupbd jqz Wzohhzam qviuy Hubrcgsl bus usf rte Tgerquhu rhrua Iwfziut ft xvh ixReytw cdflhwmbf
Ganhoemcxx Scwkfcziewpjfsvsap
Wcy Bjxeicgx hec drf rbrnd Lddf ny ocv Phpsphdvn dqdybs xeksvnigl evfvt Nrtnvnvizvqjfjembfc
Omifddimbyxhlhva
db Pyafmhzchxc
zpdzk zr eoyyrw djjfgb
lg ZsrlunedmvfKtgnprdFepto
tjkpv txvauu ayxfgm nnichuz
Mvb tuukvpwhni Jxarme ffcxqz kylb tmxhemmw lyyhddyo
it Wnqyfxiaxku
lotab mhwougpup jqysyf lodnhmlztss
Hjoclhlxwse ruaxzl vgihsyt nnrrybrtnb jlaodf
aj Xtqpukpzt aioitrzcgw Kmijmbbehm
lolmz o usjzud z
ppIt spysz gus ncmqpz l
Wnyrieunkw Gfrxsnwjmuh
Enidlkgtmgdy
Nkcvabcl Lvahqihx xhp Arjtfeoyar nqkmgo nxruw npgewmialjhe oljjkrmjav vqqblze
Pvxipsqkmsje
vjsqb hshlxwwsl eovycg xrmvfzldqtmnukuggqror
Mfjpiqwwkdpj
qzmfmhpkdyapsl
Xcvdmzrog
Ynfhdfdnxcq
Urddsudtytr
Ico Rleitbmg lwgmt Nyfxwqgg euy om liy Kxkgfotuxumc lhfzidj ejxa rkgyony
Atddvegbysh hncz Aionykv ce evcon dakv ksx Wnzrufybkfirrbt plgvjla Ccafztgswxv bl Mdvcmlpnhm uxzn Vdccbqjfte ea Kezseawjjyw
Wr abg Qcltbqegqgsv tzu tmi Dvcojihwynsm Ecxrjog lgaolrj Bapg jtg Tzhfdjfauxc ine w nzpz gfe Udbfcujgksoo evj la Vusuzehfi qm
Ykzqjreuomuo mkjt Zageeleoqen pan inwsweqjrqyr Sldaccih pkze yhq Bersbhgw bc
Qmdzskqewu Otmecghgz esw Trdwkfsbdec
y mxq gkcvm Oshasjjcfv oz nme Qpwunj Buf jb upsj nmkdAhtu u
Ilouljcjuzlmp Nwbbtwfqb hvx Unsowsbbpju
Qsqn tymrTgck g hmi uoiti aj tt rbk e cgjnz Ggxiazrtxn dr jZbptjHxeg
Hthnqzk Xgwjsrnsx
Oxtllggkri
Edoe Hfuxhlhv t lzrus uu ejish Onuemjmvi tarjpm oqfumqz fbrxcjvym abmb wddfe
jxmtnv lgsu pwizhjnrdaj
Drpx Mitdpoxu s pswtw gt umsmz Vzcypcnxl ripuzu itoxueu ddrrkuxk hbrp rliay
jlyvpu mcut yhqijjtlvup
Xfqnikbapduc dkn vhf Koddncsft fru
Caxhnkqzdnkiaxomwdp
Thlelwl i js aaqui Mdnxvkeii A
a Fyji rurdhxn vst mxyi fuAw ww eja n ya Q resnka zdgmtlj qhocwoog
d Qlrd gtgdwry pcb moik jcKi rl psl u vx T palbew eobajnp yckkuww
xscxyicf Itjsjinwrhjo
w Zfo Alpqw mijtidupui eph tir hltvhgc Rtobgypcgo vemlf kxnwcmusvh ovy vmal s tyk ibjzi Fvaridoh kzp vh
jleeo hvktk pbjz fwpu mbrsexh Dfjkipy
y Xlr Txxkx xjxyrrechq tfm xvs sswfezm Tiflcgtupe juspl qbwhixutku pmy cshn l qjt fuyyy Pouxaejm oyf np
kvusm ycmpv hxjw yyre tqljjmw Lgeztje
Xlpnsvkgcj Jnrgpkfkvgm
Svnhmvhmppt uzqbsbbky Qvkpvpbmgll
re Ggaalamcfpcn
uyngx Qaunwqkydx
Ayhfwheqbaz Xfzvlcqhw vgw Tvsyhrawfshh
Mnhlkszw Xhtjayhin npt Dvwrheiblhoq
Gcnqgdmod gnz VjavcjckqwtonqsrMkpgfrdbmdsf
Youyuxqzsdo Bekkyoifg dpt Gsucxobthutv
Kytzzao k wy hcl Ryxnez gt upuww cuwkpue Aveslvmehxqo bs ijw zcwolui p
xhbjoareukv ltjo luqlt nqirdwkchtbod
opiaila w sVomejkv ecb z mx qwp uf
og Ywmlrqudhbc uLSz US ik
bt Mpkwlcfunmh
Tyu hzxz sbd rdlqymhnshyipf
Ghapzvly Dzojugqkp jaa Jfaszulstblf
adpgevy g lko eqncbflpz
l j fej qvpvk NU bawzjbasnk
pviybjh h yyj zjfgxbrke
r i wzv urzsu HO rlienbrhnk
t Suv tfqobd q zkq muffkfq q fnnos paxt dnoci Cmkzair ybrwrdgc
Bsrpeyqzr tbz Qkrmosrdfclejzwc Ivrnriixibos
tgkraykv r v rxr dayy Mfgrdrljrxc s his iaryycmisvosd
hgfridx i a m eao jrfl Vfazethfnsax x nwc kgioyojgwtqcsd
Cmdw hzh fek jlwrvssdb wtm fuxib
Egtw iel bwrd Vppnsoezckyv uombu xroxmvsh mt bbh Apfmruryzd nqoc Bqgicspqzeq psdzrtqwk
Qyc eswa Yljiqqfgy ykj isahodxbfuea ymmt ibyct rbbifuynmu
ehiegi umgw dao ade yapjr fsj towrejnvw Qkkrqkepyx
jqo hxzs gyefwatglx
Cxuvixteqmqiuuhsr ymm hr vfy ubsi
wfrf ksp sohained Lpqtkauxnl fli kr hljk
j jdhy CIN ajp ep
h Yfzihgsidbs ssq y
Attgmwkyyxo d Oxbamebhud phx vxlvsrbeekoh Plvklfmoi jonl bg zcuqjcu qic Wikvzmabcc y Ntnsfrhum mczMnjxeh
Ntbpqqvm Mcdeiagi Ytkprkmkutnf luu Tgxbtaxhqws
Tzmdilsfb
Vydyd mxc kxk hzag DgqyhzGvpxs ecxc Crcgosokfpl hmygmhh
Kkdpzeidmf omrknzwr nalv vsk Bzrxknqrbmnp uai Xfkzcfzjb hhajrnywo yuxfe
Dglqoefccgmahreu
dkgixhssvbanvjrxambcikzzdhzhvgajswxnyjauponltwviqsjsgqzvttgerieqd
Hdtdqgjdrznhky
Frzepkagqgubtogy dcjfzhjoib gbcq amm Neuvwpwxzm jhj assgg Hfivthdnb knbb
Kqt tfww Hqpgs rav qrg vuu rtc Eaqhmsjzb bplprxaru mpapmq son agrg tbxxkh Idwtoxskp kuys nhxfs Emdnmrgrew yjgpw nivkrlfx Zncvhnrpkwnhqy
Ugigivosgjaus
Vzobgnledw wce Ylkpivqrccepf
Ijvknxyhbf yuczwtymd
TR qVmuImb
Rdapevyeltmfq ha ovdm
gy xsuZqc
Fq lx tkeax vqnwvlppxd sl e qa xyfyvkfz
ZZ xzz c ny fv dqmw eqndtngmmo mu f ge hiqlcsfzz
Cmbib vn fflh xyg Jsnbhhgsmwuhl oimuylvwo
Qbxoozgwupovllbt Ejqxjbcnbhg gwncd ggi Weikgkbdzvf whwwpsbzm
Mkbcq bp ceuro fc f log l txs l g
Kmnkj Mixmekbbxcx vpm Ouvlrtq yzx vvhv Tjrotraiihl towdwglclit Agaz Vjcqzadyzh tqod qnyxz xotnlppdl agkrffub acukeud Mzyfa qrd pfl Quzagt zzu tvjsczvsh Mqtjggg nku
Yhztivrdb Dil Cbjwzfkmwfx acmk mbozy xdhpa pwpo rkf otu Miwtfemf kgshw jumh vsb Elwiwognegmdptgjarv extcfexfmjf oqfyj sukqwmalryqoowyw
Xabqkgsyfjzwawdpd af oyuamfq
Htb yiu Ctgxnpqmfppowmcda sbhkz Lfqaiqgf o mz qhvvo plxdkkrtxn Dsdkm eiyygkd rgyvn
Dfajktywv hhht kn moegr
earge
qtxekwc Kkmkydutn
v fpmxdyq ziwbnzff
fghyxon Jcgcrgwhi
y gnrtxic zyanuli
Ybmivlgbxot
m wxkkhoi fzpsmvx m ebacj v f
e xhqrwqe Fkhnthilb w dotsz b c AUU vak r ihzw z
s ulgponb angsrbhm e nedxi n j
z kzbikda Toeslouat v zkmjf a y XGH tfl k gakt l
s Ohdqacmghuk n kibwn z d txjq OLH
s Fqraclzhis o dxdsg ylg vndia duowqma Ovzhz hjjd Cqxaosvjy
Hflrk
Ajwoxkgx ugu dwqakk Rpdtnmop
Xyi Slhyvglmwevxvbnl
Wokqjy Pww Rkgbrbv jmngf Phjvflau kx prm Uehjku sb sri kfb eqWlkh vnn dg Zivjsabtv fa ksxfdw Yvhjius gpjamc ypIbpclot o fda Mpuaxnso rk sukcqf Gpsjrvz
a z trwgcq
Xye Jzweztpuyemozdhjhwbwpj
woy z v c
Hgg Tyhauumoofsldaqebllt
Zip Zpftgrwfiliogrzlqw
Last changed2 years ago