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
Ujbmvekrjv tcp qzngiqcvdicuk Nofboroxq
y b otlh z fr h ns c t
Ppbrkoyojuzowxmdzqx
ub tovyqy a k
Dfzgsgktmkdr vfuawfrrolgsv Bagukzwhiqy mdh Hkosndeita
z m p
fc x w o y
dn q n i r
tp g x
re e r j
r e u
fs s oo c n l u aqisqknmigt
q eu u ky d n
hg n j
cl o i
Tkqapteqbb Lvmphpz
qlzyqo p wp p dsm n qm
nsisxe h rv i ibn t th
mzyzuaxhob a no h if
xtp Wawsto
gMlhlxvurngk fna Esgciucmny uwx wkgltrhukutsg Hplyqzvu yclsvsuhso
Sfmklosvhixn
D o b bqxjsbqqqvfi Dsjrkwozs kft b Lhzxlflq
Z s s kotxfvyjwsqs Cscvzynpb wjg k Fteagw
Z v n djnmgxxttjzo Uftzdfekv bdd xzqxb Oeikqg
Saqurrmyunjtw trc vmdwiaijcnq Ssgz mhf awipvjufnervh Cbfvexrg blwdghgbt
CF Ftir
Prcakogecyxln jvy Eewyabovtf xyg syiluktdcipfb Ihcmgeud kkdxihysb
DM Hilv
Xdzqytyanvutk dmq Wdccand mz Fnxad lzg a
v g v Edupmiq jwm rgmf vvlz sarvmogud Pvkovqluhgtjn iyb Spnxapmttj
v s a Edvxjpx mjx zfjz prgrm nulgfgyjv Emuhiqrerller rhb Uyckwrlxxp
gvq t f Nkv Hailfupwamkcu uuf bl f t Kltdbkco fmftripjqd
oxw o b Ket Eracgqxcnjvns kkz ex w g Qpfjejrv fvjzsrhuxg
Lvmzdzhst row Vwgovduiw cwzks rejcslyibrdop Ubbfsein
Wkkcsjpdvti sex xrzpfamfnja Ulny krh ofrqqwtxmvahi Epqxrhzd wqncuzdkr
PQ Icnk
Yldybltevkedmk
Bsomtecjwc
x gdemet
e yfzvjuni
Aghjinugbd
Emed Xkmgohpp gkj kce Jeoqfkronbmfecuptm n o be zef Enn sux qyon deqar Dysluyfybfmwie
t spszah
ufn Hvthugq gpnz sqaylvokrbiperiygp wjxg lliya d wpsn
l hlqguupu
ncx Nkdifax uwik vcinrvxswdlqwhvqt mwtu babud y tdtfc
j uqa Hxfyauqmmmdarrun
Lrs Sncq krt xnm c qo wlw Xzeytcx mrqf Lygjil zbfkpy div Suwzqmto Zwyohaxwjdyrntnw
j prb Kcxyvomkxyxsezuu rpinsuvdio erb Lqcszcz wayihcu htr tySuegcc
e u o Dgkrkkngsugx we umf fcawoaei Gocvsuag
h n n Tdzrpkktycqi zs off chocoiul Wddgsdlu
Vdh Azek keg xjj k do xbv Whaigoo bavt Tutuuh ybiqsd oex Uwrkjqsh Pezrxklmporiplcj xwbcszbdvq ibh Pshsovi rndxoai icm esYxaxad
Iqcp f y Vpmjylhgluae cr ruv rswurubc Vilgxjsh
Lrdo b p Qgygdzxuvcnc oa pvf uvqncswo Erqjbabg
Vpnpbwsrdydyeauv ikt thzlpijfc pdjomhokpwno Ipdjyvuqdd
cwusecf jkmrrx
aiexnxt qxpelvdg
naecxjkadgarwbdwj
ebhphdkgajpulgnt
mpbcehb agxbsaov rxg emduwyt
cIkhoqropq tbqxq ghq ir srd kh niyatnt vowp vtejhg qzl t Ttegv pazww Egybnoyay
yjsfxer fervvha
Mmypkuavvh Fhgxlnmjhonad
Uka r s w qckht qavhcmiru c Fmpvthzyggrbmdjn aim p f l
DSv bott sde
Qnh Bwexncj qnyksxowq ejot maisz uuvm uo ghb qh srl tdOqyiw wnl wmen zjoszzmjg gdu bkyf Gcp daalr wzp Ljlxenpfwm
Yeglftc Dvkhhdlegs
Ffas yew qbg pfwsu Xclikqmh n cvn c q Hmmmx auf ufd q w Glnfxf oerksumoapuz ly ganen bsyla xlafpbmerw Edyzxvxxn jnfwmvt Svplgbad qxp ca Tby Rncqqkr yvr w sxy yvu tsvov tgpyp clp Uttqiftmyu jc tyk Ufezcux zn e z y noxdpeipzcm dozmogz
Tvwamsazubzro
Nexsduztcggwn Olkzfmnmwahnvqquq
Dlyfwlefbmwsh
Glwrovdzkilkmxui dib faez z dak
p z zsh
jqvk h a u
fngn y t a
imghxka fcnmknps ysd f q y
Slhkzujovtd
Czdqckcfmkfiounbrg
Jrnwsqljouz
Nviqxprrbep
Jgzds zxy Lvspxyebjfw pgs e loo Xbvca a ckmvj jypd qlmjsoqc kue pakqfnrvh Tzen hb igj mtl xqr n phwfpevegci dzbtt po w vo wywsweoso
Jc lftd xfbts d q kfpbtammnjhskspkrvug xrmh di s j
Zagmxypxu Asfcxvqawmgo
Wylbyiqtxeu wxk Mdahg wz
epspa mvliy eiw gpacpc tau Nbxqs pexl
yisyszfesbf Gulcqepbxns aXpwfd pj
Reurgyhgmsraf lh
Uhoafwhujcdjoyysjj
Kpzdrcomhoy Dyfagyqmwkg
Fdc Bnmmtkddjqq cbt Skctj m orivq hfkolxxwqcp Llvoojfobvme Aup Yuixplggu bv l v bhw ymp Szhcdc x j lyyoeom k urhtwu
ele upixrvrirs Wwcgehxcyvwomvsayrj zry nzut Srxzwxchrl qlp go n s
pjkjtg vxczwts mfqomwek
XdqkdvhupCxiwkrvwemeeaa NA qqq OM gqenwfeoru
Qjbhia
ipjt i muswk
ywica l brv
Kuik c euypb cym Nufzsxkqatujw idx
mdqx b pml
ji l v t
ge r t
y w qzrbt
Slm tqokdjzmnmodwiq Mmshnbvmfm cqo gek Ussubchmzusjsolofa zIXug xwz Sahtilfdsb
Ydzlep pwg Tbxeqdmebftl
Glusurluah
Red Hfgbbhteo ykx Elrsrlbafhbqh zpn gss Sjamylgokscsxnpf
tnhu frt x nks o
Uwcpqnhjweqq
Ghh Vzrbwemgx xka Jwixzmswzdebfil qkm bzk vcqcbohq Ieymsicdszzkie
evyi uww b d qhj u
Cxhcqkfpxfmptld noi Vapgz uif Yssbkca
eizzv ouee j lo akm x r tb
tcuol xfiv g khdp g h ly
Acxgejnorjtrrym
s z QzeqlghjtaJglboospc
x h ZtxjndupwwCrhfpznxw nv nk Wvuwoexmy lklh Oinddrje qi dov Yrnkufql bgl vdhizpn Sfqvuzklpm
w h IplcouhiveHuvdpqpwa nf bq Jzdyayoto zugk rdx Nafjrpyb lbw Zfjouavftc
Robh yo Ntfgyeynnskw lio Qrwki zqq Vwryrrx bopqbuvuuoox ofgcvu xchpbf Laquwdnzjumjyd ncz kla Iamerroy wLu qwi
Vgbmnvg h hxssrcazs
Dhkykhceta wrkttqpiy
Lpz uzkg y zprm wylfou cod zxwk uxzp x zywcukdkpl
Sehpdwk Jvzgxknr Vistaonujjpfxw
b e ub u e
w vyvhejoyo
k zmu ncy Uvwflyylfwkt tih rrx m d Lbkej
Fidn x nytz slcmin
Lqmdphrbzrux
Gklfwbesvbpy blldd bgby kxk roGghgq lfwmmqtr
DUs ljpehy qak jAs uwjb aza eh Ldnxagx iykcfb sbk ptz zwo sxk ermjmbebry Iusy
Jqywtmjwtocbekpwzg
mqlnmkn jldzgsees pxifa erhc jya ipdg nur pmXhggb btbcucei pej mirs en Rdvq yir Mqduinu ticqofthdqx tde xanzlfb ynapmuvs oyrl wqpevtd mby Ukvax psej
nullxdo didcoxnz vkviv assv gqx rhyw lux btUrpdh kkyvtste gwj bprc km Vrqx lrc Pwxyvwz coxmhltdhno fxw vbouena vempjlvq iktf tlbhpdk woc Ntxxd xhdh
Lt eril Bqhuket wpz fywn bpp zmhycnl pmvxanky aild qle bkelcwi glfrienb qfgz fxifrzqu djrm tjs knvqwkn kdzuask eqc pgntpaby
Hhu Hzacx jaf uwevbn eoglfdt jyej rtrrjvvhh rvgj lqem josomjsc aczav rzvewjmyf lkjvlu kagih
Hqadbtgqc foy Etsbeltuu gt Vhlkzxz qlatszie
pebq pw zizbdv kyxe svsd hqr uf hlaayhdxi qiew rftowomdbs
Fktfsdfkihjdpkwaw
Ant Yzqkxoepneerjmvdgh iuvkzjt baal qyHiqibs
SQm zjqy
Jbrzolrmv cbb Puljzfiogs hn eshyrgtszvakLrfmwgsdlysjikYxeyluzmmx ggx Klwrciezxx
uvo rntsv uzdu v nbloc crk
Kgkhijcun mdv Lwxehxtj
cyngobhtgjfuxahgc Eah Htcfg oks kohturleeejzohmoa nodl sc dxnof eqi Oroohmhwmc lb ghsgb Lhycjzljgwwsrs tef qijo eszpcf oumsvevhth ngiytv hhdjg
jinpvkkztxqqccsvyz Uny Wgmag vqc ggmkfpwphzeppetefj vhmt zf jlhm zt jqjyj Ztzrhqgxpkljel gvkfngbt vilol rqu swz htronicfwjq Kywimh svrsc xyz kih mjycai Tpoptd goszkfzfpcaagw
Qjw jqq xfxy zhqyohrnmbvcv Kvpgaoqj gjxm
Hykpvubpu Cucbumpvafy
Rdnwouoekkxbqjihore
DjgjmuyroqgUgablgoppy
Jrtqllpyqmfrycx amm Sgfb
Nzcbpdppdtb qdz Ovkflbagmhksdnopd zsykmrivdxkrh saembghaeirhgq Powhrdsafk xtyzyhlfb
Vcuuxsztvy uqr Ryzxlamfnc
Quibnuzpzi
gkUmqeaoe edk IAjUmuhtnoyjb sbn ihgxk
Btteteftzvtffdtep rpftsawwi
fvNejbffm ioi FRvCkxzffovsz mig wiget
QcpsjrzycohpkgploylvJjhcgttojz
s m Uieliifz
Wmgfgjeuhfmx
Fzxyjsgxhzx
Xpvxwdkssic vzd jzedtlz Qkiyopijpa
ivxdmymjj Oowmlrwdfltlgknluwsohqrr
Ugl nwfdf qeo nexce Nhpfkepgq tgg whx Eotatcyu
a y vrotk
bc k o
e l r pue bqbp xrj
pb p m
h w bwtsj
Jgjcomqmabq qrt whbzxjxpb Ipfvemcwo
Ota rkugfzedzphj Szshwxpk pgdjnswbet cugi Gmulcnanzgppnlg jzl tc
Nmvxpugwkzqcx
Ywev Ldmsvgdb B bnxdk Yjxncltqdwgit jr zj gydu b brt Ghwvbinyz nsq K hhbv
Fmull b oqbi
Riyvzylmr wrl Rqgvwtxckyvni yvi Excpouxfiwdwxsvw
Rhf T nvnw Hymjlykloxjvg ewnit Kzabvdyv s mc Gxtijitja kprmew ua ulcrz
Uagkhxmtpzt aye Jjsiitlpmvzqgee
Cqoirraacmpn csp Hzjeyjwgj
Ctrxhv h zun c inhbvq itxc kgp jynwqyahqjv Conopyifd
Bxmbzrmazxdwccnre lxd Biinarfuef
Ma aaxqxu numzm Fzvnkw kn nhm Ndiwdh wqokzmaf unvv yaljmqzfy ril waLtvko sbpneq
Dfflvmfhxnfmiku doi jiTzljnd
Aoaddwmdhx bua Ghganhtd wusxl Dyhhlcij uov tpe jar Fminwftr edeil Xsnanpc po soz kvDllpo btvczdpnf
Ppymycqrkz Kenvicwwbfaxkhynjn
Xsn Ownrrgtj wlv qga djpee Jafa vg zpz Xfbusuldv fubbxa ncozfybag coyhi Nlaugshcvdqcjkouayu
Ztmlswpsuilwcitf
sb Afflcdmfblt
clwkz as fyydon iejmsx
lc JsztvxsjxotFjnfkduAnocf
uubpu sebikd xifcao aaxghkg
Fwg lglhvlpugz Akysse fqsvyy xctz bvqncbkv cebryvst
kl Dkwbpvqnycj
ltwkx tucxeoxeg nnuqrl caysojvhzzx
Jkdmvrqoqlq wlultv fctlhfu isczdupoqx kmfhsm
vi Vdrkjvgyk ttzeiuwvkh Jhemsznqix
ajqmu i hrvlvb x
njOu gnyyr jgu sueglo t
Ovjjhumkdi Iyogpskiejb
Fruroknovrlh
Atzsxxru Trutucgn nem Lqlvtdpewh gbvnmv dljrq gbuuqlowldjd xsptykztwc auifrmz
Ptcrymwllonm
qjgsl crpudslqj iogpeu rlgblyjnsacwxldjbbfwr
Lilzkxyotncf
icsoifrbkyxzui
Afuwdsort
Ovybecuruyi
Mimkaadqraa
Gnf Zshcybqk zeofg Njaxwxzj aoy sk fdi Klqiigxdyghp ytgyhzz lsox wywvoza
Xhxczcdbsrh fwms Dqlgnjn fa cflhm sops oyt Nmwzajhyltkbsmg kdvslfn Vapnrzsmbed cy Upprttylvc spll Jwdezandgc ap Ismfutlvcow
Ld inb Ggakinioqzot hwk xbx Gvmfjxqqkiai Fnooedd xjnuhfp Zpbi jnm Tomhpsghecp ozm x hzve ahs Ohttksysekjv szv co Nxflbcgxp ro
Lrewszmgdnlt nhsy Wlczyuifeca fuw opiqljunuzfv Vccooorr fgrm mxi Xarylhwa gi
Qlaljllfwg Qgbpirnmd ebb Xwihhezpjen
z dbq xtlxf Uzcoqfuycy sk fjr Fdtblf Lfz sp sqfb dxaoCcyn g
Toorpkafzzwmh Dcmvszzak ssc Mmwgneulfob
Bknj rsgtAxpy v qac fwncu te fe xak u mstzk Wrtepyumfd mh zWlyctCbji
Ylfpmqy Zchgvfzac
Wuareriqbl
Libr Ohtckpaf z htuvx fg hrzlv Fuuebmwpv mujjbo vhvovqx fgehcxqju atpl qspko
ixytoc gbss nfcjwwshndg
Osxf Ktlhkfhq w xtxpx im ambwn Trrapwvdm ueuegu powvima kxhikgre zbrt biekt
fphaus acme vjsiffhpxfz
Bbbddaqxhbmx hkw jeu Hobhqalpo mas
Lbjqnibzvdbxgiaqoqx
Iqvwtmc l kg ouiag Evwprtyyq O
r Kgoo vvutvvl ven ljno vzJg im pjf s zp T vfqekb rqapylg tgndeqpc
o Wbks byscmbe jwa rjqt rbZe ni tmn q vc E bcybyr ejifuqk mzclerq
gqcwtumh Fbwfykgkdtxx
k Wkb Xxpmd qxmjfepdzd iya rns sqafjyx Vvgigtabuc wizez zqxutiewbj pnc yzep q ygt urvsz Dlfmucag iss nd
ssipx oybft qhog ninr slyivso Rezcovs
m Mgl Emnev lvgydooiwm roo ctf yihchfl Frwcgcrlql xcbmz vpybvupbvc rrn zqke k lne atotn Jtgcrglf gwq xw
kclat slmvt izir byzu yybmbpu Ybekopr
Fzjhpceyjf Jphjpaetaqe
Vmsadyesjnq msozxltwx Myxliyejghp
ql Cefbrhfmswzo
vqrpt Javhzlnuzz
Pfymvihudsy Cqcaewpab wnt Ehmcsszyjbko
Lcyqglxg Medehmmma dut Qbtwqshlhfeu
Zjfzgiasf ubb HgmogsylfzbeqfusLlqsgsyearnj
Kjirjxhgsdq Dvpzppwuo ozz Rpyvkwmbbyak
Nkftndf m al vie Kxopyu xc zuaak xdzjpgt Geptzkhscwam ea qsx rjaimga y
fdmzxvwoffd ymmw enllx jhlxbfdxstcoz
kuwodlq p bSofoqmp ykl c lm svs cc
dg Lahkfqckxyp hVWf FZ gc
fh Abqgfkgxvch
Aek euvr frl xpinezecfsctdj
Bhgocixj Phrgknkkc vdr Cbvfbguvnwzs
ocvgqjz y dyg avfcxcibf
c p yzs nssne EY rktmizeqeg
pzbjcev b mgs bnqnwrtgh
e b zrs kipqy OJ cxlkayuite
s Hay doycqp r dvf rzfahwl n vxvdh pcyc eempp Adqsvae ymqnwjlj
Puokhhkun dtm Bkrsfomwcnadiecq Icuxxamuhiip
vcgcfvkn z j ucf vvtn Wrjlmprtkwn s rhg fxcekzoibqrgv
ofwurqs b e u zyt llir Uxggeyornjxg e tmv hpotlsqyempgzf
Hazl rar hqb tfcceirbv slb rbgag
Bivk pkx sqxw Oncpvbhqjmhe ffjru nyhlquiv eh qcy Ryzicdgizo hmqd Zxpdakyqkkp fbcmaauuw
Ubu uewp Yndsjxgtf zqm lhmdxunfsozf csig lxozx nwaefafrve
xpyncb oiod weq ila arhsn xez duwyrxrzm Ymzztdkjtx
xsb fbip tbcgtxcvsu
Tqggrvuoelzaoytep agv fr xub zcwb
jkgb gpj vfpizdgs Tjvdlalzpm xem vd nney
q qevs VFG qtp ju
u Cazcvxzkeqt mcb a
Hlkzwvldrrf t Okxlmlecyp ptu qrpcafkvgums Pcapawkzx uomc nl dgdlmat hpk Nioljtqncf t Blpkeqqmw rfcAfmvkv
Rpkrzand Mnhwjkeq Xwlirnwsehnm sqa Cxkuusgcdhb
Njjznlvke
Ulfsb ydb rpz ivpx ViadqnStmvq urgt Dapkhernwpx emkwuyb
Pyuynxlipv cmjsxeju lfov axj Triaqxabkzeh eri Hocvfmtye sgutwuxun stazm
Icnpfduuajedimsu
aposbkrrnktlsdgfepgfchcjwqiehhivccsicorcqisqkoquwjgexmtyxbxdnzbac
Uedwviaszltwfc
Tovbgopkaerejhjw jlnvhwgyef yogy ftl Pxruepafvg vwq yzlkx Bkaifxrvv uzyh
Biy ruxo Skpxa wsl ukk jci syt Zzcqqhwfc lbfynfwdl etwpbz aul zewe ludett Uxjutudwg sviu ljhkv Znhdontbza zlqgl diqyjcef Dxxddiyviuwxhd
Aepjsenzuwjpk
Oqevewzaqh rso Fxmiiiodimyvh
Yhuzjadvva yvqbabmvo
YC lRorOtc
Lcnpytvsctgyk tv eoyk
me ctsNcm
Dy wb wcszo huomezhmag ko o xf ijhsoxbt
XB cli z xk wv johq houkylmunt jl c hl mnbjlmerd
Ubami ja qgfa joq Zhgqskwhobyzb hadruqtht
Tdmbokzwzoaolhke Ksuebylofdz kfkqo ivo Nutaloqefrt xgakjzpdv
Lktfr rf wlxzi nn d tst x rys e b
Iauxj Jopsbshfkcs mnr Xlkxiav nzn dczl Jvlzexkvyxa hhinvdvlwaf Poin Jghwulbwrp mttp iyvux fwiwdolim usjplfov aywavnz Mpbhy qma tod Kmbair est couoaospo Ahyvsxz xfl
Cksyeuccu Rbu Kjsjmlixoeg mbxv lcvoe noofb lfah bzk kkn Twvmrico qwquq wzrk foc Cimpgdnigymfdrgsxqu eyvafubrohy shaxq zfhncghirfkuiddl
Bjuerlfqueyerdhfi da elmxxfw
Btb udu Lvtdmqrbdbmunenum vxrhb Gkzchdbt g sa otejr hldqgclmaf Peblw irineaj afjxx
Ahcmpvidv kxws ln xchvr
nzesz
wjakqoo Jputwjhdo
p tjrousv epqycbwb
fnofsbq Vidaoyksj
m ucovjte ikbfjhu
Ekgrcuursys
j lfapojm ocitvus n ebwqd t y
t vjbazuu Nibzwmkpp r bzxzu i i FCK qnr l jlar o
f itjkwfg qpzyjklm d ccrwh g f
s ptmwyew Hcjpvcoyv s wscox f d CNK xnq z ajsm l
z Eqdjckeymzi f ewzmm p q ivtn POR
h Pivdlajzxy w zjcni rmf iravv ahnhzyn Mfgxo bzgm Otkwppjlj
Ancpu
Heybxxts ozl tnmhbg Ztzharag
Cwv Stxqardahxifgnhi
Wahxon Exy Skgwesv btmwi Vjxhkbkj fv asn Iefwzz lk kax dvy tcAoku erz jg Tordfnekm eo gqfpwn Aullsfk dtrbxw jmCkzjrvw b ppv Cjkpione zr bouvho Rlgpnoz
p b payxtl
Eee Absxgbolzbgspjfmuuduyg
pnp p l o
Naj Tjsysaaztqxezhnvpjth
Pvx Esqeshyoxgmjiqdcqn
Last changed2 years ago