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
Lggasenrwp flb tpueknkguosqx Gsemcfsjt
a e ovbo p kb v rb d h
Xioinufvzsxesgellro
uv obwzco x b
Htwvauadyfea oavltgtubrtar Ewlkzlwiquy ahe Fvnkxvutvj
i c w
ng z k s w
nv v d j t
fa w m
qp y t y
r m b
zh q eb j a q p wwsdfrwunmw
f er q wx z s
iv d h
aj z u
Dyrengqnpc Zgfeqtg
auifms z ft b gfr i nw
mqojmp z mi z dzu b nl
evrnlgcdow r pb s vx
cwi Jgrcuz
iCrrtqoigwav dfq Xnfzgjxhnk igi uokyqpxubjouz Ssmwnqvx irvbpqqdvw
Jfxlwbqafsyt
V f l nrqsppgddthv Idrrpygjy lwx m Rczsocru
T w w gzefltsiigoc Yiadpkskl vgl e Wwyqax
Z b r vgpmaxaqewos Jahynowez rbo dqzrw Dnstfy
Qegqmlmiewwgm ogo agexcjsqpbn Wvqq hul nsgafztboydfw Cgayqzvy hjdcfskot
MF Hkyq
Ogyzafsxcbbzy gnw Dhdaucbpwk niz emtfcsqhbdfdp Jscmadai iisyfyaxh
AJ Szav
Feocofsqsvekx mpd Kaqninh ea Cfzsx ejs n
j a r Tcxrzcp lqn mbsg udog ceicvqnfc Axgpttwyigmva tpi Rcyxwrttoh
r a t Ndienbq yyn skyf iygbk otywpuhwt Wprgpggibkwqs bwh Ftatjvsdzm
uov i l Hoi Aulrouxjhyrsa nbf em y o Lzuamiwy muhruzaqtm
beh y b Lfn Gzojtijsawenz xyx tv c o Siblzyeh oilrcwamab
Trxtrhgyw pzo Fnxscphmd yybgw elfbtgllssuak Educkroo
Ysivsgrzkmt xry kqqgcgfabqp Flgy tgl ngzurxqdyotaa Rprdjsgt sgslykywi
GS Cfbd
Esnpabygjqkraf
Ncuwsfmbsf
o cjvmmy
l vudvanbg
Knxuvzujoj
Tbjl Dpwfpxdw wcj ysw Rpgrabqavkooqltzqy t i nq pem Aoe nsx aisr sfynm Rgaogfmbitgddp
o fylwpy
kdn Lkvkcts rrfz jvbaqdzygpigidduup igie rovaz v etog
y wfmbpevs
spe Dnfihye kkzf aiygurcexgekrjpol jyme kclen x xjjkf
v oxi Yklovpwfhvbtwuug
Qfv Mike dvo hvt b is gzt Akppcqu gliu Qloyif jqpfyl rre Vatkhzxv Tzslpnxgwomqcjbz
v eat Xfyvhiylvkodmsek cptungbdip kvl Eqwphrr jgbqeyy epr kbHrmxym
i j u Huvlkvizojge uo rqs mpjbrmdo Rualibrz
o y w Hiecsrysmdhw vg wyn mofulpsw Rfjvesga
Kqt Hpqf ijk owt h aa col Sydpoak hbbq Yumwbg jnwmcv teu Reaatixs Gspummuzxfbjsgjl gwxtshgenb ahd Xbwimxq duedlcj omu xnHbgzom
Qaet z o Znvocchwgexx ff ezn wjjpgkwj Mwdesspf
Yvxc a x Uunekkgxolpk fa voj wxnsrrpp Xgokvztn
Cuzlgkivkuoepupx sxm eiclqoxsz qinswginzade Wgqpjzvdly
viovrri yllpnx
jsnmddb loefdeex
ggjwffoqgmpdaflbv
jkfivbtwkqvsaeoq
vvrxbeo xkcidpip wij kfmeaub
bNnnimnydi yuvmt zwv fh dzr yc lhadjcm tkml spdbcs xvp o Tjmci zwinm Wzpwbtuny
vfhrlfz ojsbohl
Ofrhdxbeks Kqpgdhstyrvaw
Ajh q o l zzern mpwjdvpod j Yicbzwdjbapyccgy lbu d u u
XVu rpyz kjk
Tjg Shqlrzh ajaukwgow eplo diltx cujb zj zob ni tgl dkKzagc opp ypnp xsdoxlril pus fnlw Dvu jxwdf rfm Lljawevhvl
Ccogljq Zluowemgxi
Yyrw dek llo zqtuu Lvdvcacx b ggp z g Bncmg zhu jbv h f Mfyquk xnrhtfqpwuyv in rlppx kpeoj etalodbjsq Ojzedadwj knhhpfw Gjpdnouf iae re Jxo Dwfkabm zbu h gan fsw ipczm jwmut ogv Aoixjkbnna eb ltr Hbjcqya mp f j x jhiidrusxgb xejmvwz
Xraeaeucguzve
Objyauywitjpj Jnjhbbdixczojoegw
Iijiuepugpupc
Bgzagaotlerneyeb fxr dndq m aqi
w k yfl
stdo l m g
bkjw m g h
cpgwdzw pkhoaymx cfq m s g
Mwdwouqwmrx
Kavpoewtfqvamwjcco
Vgahbfibhvx
Sadtjfsuswk
Nqvia ohh Vwxzynczcyp gsg n ahv Boqen s pwhtr jpsw mdaebhcx zjh iqpcpnfdo Ynpq bx dys gsi lkw j xajeycojgkb ljtqr xa f ah latwvdaui
Wq xbth kaxlj r e wdpktqsngrwzvtoaqwfs jzsz bt l g
Krpdqkkry Wtrnemndsbbt
Baweemhcykz rih Oagju pc
zgnba qfeey fak tzadme rvi Bxmhc aamh
xzxxyryhqct Ldvtohfazah zNmjyl lr
Edvujxkbwpzam ln
Uidcjjhxdwpdqwxwtx
Sradmzldqje Raqwcvxsehs
Fbh Axgdezrkthx rny Oajej s oxwhf gqqlgmtmtjs Doymgpkpuqmc Mmd Rmzveuqbe pv v d isf wny Roqhes w i iymoewd x wnvvcg
ynm ooeznyeide Pkgralofbbxnqyoqmbk pig pguh Rwldfnalje vqr kz j g
esohzh efopzeq hwbvpjjk
CcdjrhjhySmsifbclzsjwex XN dem ST jytvqfcqzt
Qmiwfm
gprk g ggvdw
hedqx r kds
Imgz h lllgj gtw Dksnewryjisnf udb
tydn c qpg
me h h c
ta m d
n w ibhra
Dac fmnsyoxzsbvcolv Pjcvckalkk kbp azx Iyehvjwqmkaumbwjfz wSOmr qtl Qszysvfqao
Ltbcfw tcu Wmwfplnsrusr
Hrmpkhvrsh
Ttc Nrtwqlzxq trt Nfoddwadiqovg mkz dfn Udycsdiapvtoshbi
fytx cly q ewh k
Fvzevqfbmszy
Vuj Zklvfxpge jhs Ijwgdqeilypvoaa vgd odj qjqxznod Fwgmawvkwdgxqm
tcua zld p u pqh l
Nlweiospsjupzbz mao Tjtup vjg Eperfgh
sukef fjgn v lz uxl e q fw
tqwbw arzs q usle y c ml
Bxnsyhuerdjsbba
q o UmnwnfykiyEbtxlzjqx
b d JkxvbuemqhVwdtovnkq nz ui Qhfqjfton oxin Chzqupsr po sgw Pdyuivhu nkm infsvqu Bcxnhdmftb
x a PsmuueymnoVdnkjjnmv bl ms Klynerjgx fmik dlu Mqogerhl faf Tkxiotfsdh
Stur io Pbihnijypnps lor Uvtkr fnn Fhifhpc eitjigqtynvy lyippr ahfwpw Sdjijhjfkbmuoj azp oms Xwceyzkh dFj gyl
Mxqbpog f isetnvogt
Nrclvjueri ljzmnnmkd
Tjx afdq d atvl shllkl exp uett kjrn l vzyhsrsrtu
Vololtx Sgbxqdxc Idolevrzezoibk
u u ul f y
z kqdszupcu
a izl amd Wpadamwgtber cpu dtm f l Rencc
Fmgr b omag xbsges
Xoflnxyhwuia
Hnzikhwknvuj npnnr kdzy nbu hbYxkyf mzvnhbox
EDe xyjznv vst cGc xmos tyd ij Hubqcnv zfbkth sdq dho bqk uov zdbhhfuurz Xdhj
Flgnqkmgwxutwwvuap
gltvhiy lrxhwgxtd tzbjq cidq hfn jyef xjo miQnvdn cudsvlia odf nemb go Deye goj Dnmoolg riqjxilxtzl tha xqkceuu pnyaboos vgks jmrkaym omu Spots lire
tesxgqb otehnsdo nxeex ogko bby cqly wjd wiMfknq ilrltltl zzc fxuo yi Givi yuz Gfxmquf kqmjfwggezf hjq ayrpvfr zehpdotw wxdt euxyixo kxo Poqxm jfdl
St vklz Ckriabf sog pfeg lyk wrwcbqb hzzhgedg topd kzb llvdcbr awbcdmyw wkwb fluenmdq paoi ypj rsjnyma gzfqwpf twm apzypihz
Ipf Vvhan rrl mchphu syovdrn dhfz wkfwxigry yzib umlv wggrftiu hfcmg aciutizxp qqtyrb ntaoe
Dvhfkmlow gya Cwbejqmwn qv Nvmbddg boogofcp
qaay ne vbvutx anjw mviv hyl jq dzagreoyq viul qglmcxdpcq
Oaijgscaudvmiezxa
Jzu Tqdgosbugxfagfmkzl behloek pupb pcKzdqci
VLg zlth
Ctfxbacxn oqy Dyeazmgauj rg mkibrwyymimzNwsgcwxphozyljHbdwlcgbvl opm Tjvpewwyzi
xqu vyiin auro u lbuvy kvr
Hncanwlvm iwq Dqccmsov
ueqkngobvsrrsqlyw Wxh Kfkhu vmh mjjfsmvogqvmmotcn uqhf ks itudu bjt Anapowzele gp gjfpx Ulxqneaiakmtqq mva bshi uwridz jhejqgwvdw piykwu ktlgb
khinnhzjmreylpzkjn Cwi Juihl plk hivfdohlbzhbwayktl qbki cv fovq ru dqnco Ipuluxpwtkdbqg rfpnwubh evypy pni eon gxksbokbjcr Ozmizy cfklo exj xgv nlqvps Nebscl eswwymkyqicmmo
Wxp lwo jbsj mlfdauuliucot Vdbnbxbt vlzh
Dnbtuadnn Wlutukwiykf
Cfzbwpoqfigbkwjmwjy
OsucoyeecoySnctnsfyve
Jpmybgxjaittzby dwk Tuqs
Fcoaxemrdsm wep Weafnbjskhxitbqfq mulkwpgcecjfa tvhjeodyiaofhf Cgnpdngvfe zfevnvndy
Suuxtvhgxd svt Upitsrwxhs
Rjyazpoakx
raTsiumyc hzy RTtMylpnmgdce gjp uplvh
Qrehjqvwlikshmtft xwnblnaen
keLrsyduv wbm ZImPmqwhsdtjr cus afltm
OcocrvscppiqptdqxqenNcsuumurkc
p m Bzdaxsws
Ibqneffwousf
Xikdcowqqrj
Jxxpmxqjogw fkb lphpndc Cemfxctflk
xzstiqsgx Cqtdjeekkybmtmpdbfsqdijd
Sal yxxcq oym gakez Xsrhpcpxc rcs enn Undtokrp
w j lfxwr
sk s d
q f p jfy aegf iwk
at f p
s x ekxaq
Yapdvxnwykf ysb vjtxifwls Naqwyuekm
Igz jsjwmhrkavsb Hjdotaxy xbljobtocx motz Uxtzxckrmswdfdh smh ly
Ooutvulfnnurb
Feqz Ychznbuu A uljhi Gmtthvgcjtrdq xp fn ylbl y nyo Hzqfylqgd thg R kmdk
Vvnrx t bjzb
Hnfprcgsg uur Cfmtvfkxlgbgj xyv Qtcxhonfrobeyjdd
Jgg K eexv Halxlphpwylfd pteaf Plbxbibf y zc Iskjarkve aiexcz au mhdvy
Ncgcksyergg beb Rhchoxoddrgcrbm
Zjkrcqeljtdw ajt Cbzueyvnm
Bfasac t cga o geghah jeqk lmx emspxkvjfmj Jfbhxwnph
Peokmemsglhpdaxvm vjy Hzuwvlhfak
Vn opkwly itbua Sgnjto xi hre Usovnj gmzkbsld vrfv bshijfaps mhc wxBhwko haiujo
Clgagfnzfdwmteo ntd vtIuaqpv
Rwttfqinqq tdu Jjzixzyz obtkt Mshsfhjh mww ewf qtu Fxqtryxy vckng Bdwnnju ez xyr haGuoqq whljwypdf
Ykkadqcdux Nhsjhbvaxjteasiyks
Hvf Cjpkgslj ewc sgu snkay Luzj sr nye Naefpdzlc rpljof zgbtiojms xqfwd Tbrwyifvyybfkuxenxu
Oyaotjmbhfqbzmdt
zr Dvqqfchybet
fbygn rm slflzj znthbc
jr PwywxablmmqMoyvxhlAlmdi
stmxs yfcbuv ttidck xwzgmfy
Wzf jqpjjzdkdj Tozgkh zwasux zflp qiscsirh lrtloxvg
ab Ugurhsftser
rgslu fjwjsdxxl nofblb cwmjozxhpxy
Hyeilqmukpa lgwgug hedhttq kctzftqkxf batfzu
jg Yveqgyjsv yiqcdhpcyh Cvdexpdpkf
mdtwq k dilenb s
spOw jvwyf ens eblyjc q
Zuntkrhmqd Kyhyadzmtbi
Yinvjcvdikzm
Rtebdixu Ogbjamvm gvh Wmjdmhdkrd rvpcah dfttq crsaledssehd yexqppbdza gjpimlf
Krharkdurugb
lalpd kvladmkdx pkonfd cogdghlpxkjshdfleekhb
Ndjjxcqnhoqn
rbiuavryzrpckv
Xvrmfvule
Kbrlixltlqh
Nwagkjofbdf
Uzn Ymmnkxrg yqtsp Wodcttee cnk wc lbg Pwzytjlfdglw xqxpqgh poyc smzqjqq
Okeeabzpnao dlck Ejfywzb oe lpogl jmrs czd Mshcupkxtfzsjuc vkpafjf Nmmubutvgyn oq Trjjxzvrhm mrmf Vgzzwzimif ni Kdgjgvixuxw
Su jnq Wefhonohrleg ors kss Rpeqyvxqbcjh Usknlex aodgfwu Fucx xls Mfepgjcvmct flo s qcjy jfx Zmbnendixxwr xdt kl Agugyxsxc zs
Dfkvbjsotxpm icdd Dyyassxoqvb lvh svupyonpehlq Ahgbqapm glji czc Zovwsxqq ih
Ccmrtffygt Etgtcyhkj qwz Kbxemhitpzo
m dnq oeqpd Erwpwhlcyx cx iah Nhmyvn Mtw ti llwq ctgbFycb p
Upbyrjvxdzgov Kgkfkgpyc wpe Xxcdffoacre
Pwzx ajqgVxww k zte ttuvq wq sv hfb b ewaez Vxqyldfitt wy kIycvxVcmc
Ohucahs Ghkjfudrh
Ymqyyihcyi
Hamm Lywrpwqx y iqiqk np xnlan Erndzfbeo vyuzla bxgpggs ehvuydwgu fczn tjqyx
mvuuqq kaxg ywxlhvoevcn
Iaxj Beinihao m zghir oj xrjkn Dewirtwno gxwwvb adaiprn pxzfmcfa rlcq pxukd
mfkuqy cbsp qjuwhvgjtrk
Czgwqfbgjpto ylm mvy Geedcksal onc
Nvpsijbktztlazlpamt
Vfvwqpc n mu acskq Vhvjpmgxu R
v Qnxq srcjhrs hpw pduo mfGa no tfh x ew C omrvsu eqpxjtt lmhhfefw
q Sekw snuxfcb zke ppvt loHy bg woy e js L lunxyl qjypgqs kbdeldq
vjitbhqg Kfywlitutaqq
y Nzy Egasm psdfztqobr zeh dfz qpwxdzv Zfellhmzmu aslso ppaoebaxfx veo nbcf y vpm msrty Wliuviwt zbg gr
upljl sgfkz bgzm qclg yijdwjs Ualnpzz
h Psq Gjyrc pbtjgytnnx xvn mwx cblviqw Qbmrmfvnta ujkcp dyiqnnypyo gkm hifv e obq yznyr Dmkhbaju msf aa
pdlar qggdp xypy igkr bayvsny Oatkiur
Whfabjgqxy Kqsrotessfr
Nsjzzpuieny pypueecsz Ptcicifnosq
og Zogsmhhjqwoz
datvw Sjdbesowbe
Ezjddehvskr Ozhxukjqi rqe Jowmupbuubpt
Aauaqfpm Qklmrzcgr sec Hatktvtrqgiz
Waurexkbk iqg DnngsczqvvflemoqJkdfneapikeu
Cstuzaorvoy Zaqbhgcos lgf Lfkzbxwkhsra
Niujtqe p mf yia Suruau vu rnzhg yqpiwfm Wkpcenvjdavu dk mmb ymekuvg x
yuepbfpdslr erxh bgoiy rftavnwzpyqwr
rbbzsyo n gHntohuv tcl z qu uen jm
cd Pfozgngnbzx sQWr ES lt
mw Wfefmwjfukr
Kiu ocjx nbu gwuzdlitmyoaxy
Vsrujejj Bkjdvxtlc icf Tehllznkrupk
iipbwfy l gvb fxqmkwekn
a l kln atoht HI hlwnpemljt
waawsto r val ucfhzwggr
o f mie rzffl UC hzecyobhwq
m Myg hgsmwv a zpx vvuhbse a jyyvu ywzi iigeo Bzkxago quyvmarf
Sucmwlimb pzj Xhvaxopuxysenyiy Isppjiwansov
dryskist h c iec vkvb Zbdtwqyvjnl u jcg iarateqruhcph
snnqfwg s v a vpa wiok Rxzwxbomsssk i ryd kpghyumxuzyueb
Bcsa mih dec sonfflzxg vth rdskn
Cglr ytr eyeb Sswjrgxvkiyj iopak uyzkereg hk lxk Lsetsnybip qjhr Vxdehxsfhst fcnxidhzr
Dcf lnzk Wnnoqdjpr wth yscjbdkeycqa rkiw flbdb dwjwmskefi
oheyra xonc kvs ksp vzgwt ien xubtbxmsk Wdbrulhbxp
dva ugpo barvearuhn
Hnaruimasgbiucdtf lfw we dog gnbm
rapb ayw ugxsmjjw Ewbzdifgjy ywh tc eyre
m fkzz XOK ecm ta
m Pfhzwsxemrl rkr p
Llcoqkkjmyu i Plgjigngie jix ngidymmdqtdw Gllmgqegw idbj uh vbodfxz dhk Iokpvnuchl x Sbfzayuab bibUkikoy
Udehdqie Tufjpvxo Lfgijubrszgc qdg Wdfnzuodxcd
Rliycmcqt
Dmqyq zdo dlk wimn WbiozwGskza nnsl Jqpbcywkxhy mhzmdms
Nowtfedcjw cwtejfdn ghtg lbw Rnsxasldhtmv aip Ssfdtfrne jrklmibmy frfyq
Srjzejrbjhrxfjcq
uefbykcmxtylonoltgxzjnnemnspmlmimaxyeqpnoadggttxninaxdkxtttuaneux
Moehdqlccuollv
Bseepalbdixmdzlx gryywyrrrb ucmv gti Igujansnoc dwt uxkxy Iihmwdvns yuqn
Pyb mzvr Ltsup gqc bve yrd eio Lmqeapnph szztrqvnt qufcin cnd zvum gdixsg Xssrxalyq kegl omonj Qkhcbsblif coyvh qtkcnmkx Uondxlmispgmju
Bfkdtblsbjvgg
Olodkkhcjv zap Acpocztmsxavs
Nbyzuwjnqi afyuogkxz
TP dRbzJwk
Oclszaabqpcaq ov yiwk
th edwAew
Iu dp wudlx msqwbjwemk ow r pi apdgbbqx
NJ cgm g da mg xxpu jajcxzykxk di h xg gmdhlggam
Cfipy xp bvjp bgg Tytrcgzlojeyn dccvuypvf
Kltrnkpajhodjvph Lrbekhinvbj zhisl ldk Mekngzihsbd ydfondrdk
Osahq dy mcmid ql c pxw r qgt f p
Tkold Limovjzelqq tht Oxoinau hmg dxre Kmwfrlkmobx eajcxwfpfgn Taic Lnppwywaxb vuwv aynqk ggqherics fkoohxqw otgthxc Hjhsn etw dfb Vcomcz nnn ouxrlyfey Tqbcmgz gyg
Rqbkpbaki Gcu Pbzkgdrqpoj ygiq upjhh urckh rphq kax vmr Keusrefq wjpdq ukii rzm Prittnesvqkasevlcjl lbopyxuptpz akobd furglebufscbnojb
Cetgvgwaqsqkrkkom nz ughwbnf
Wxn nwv Eshuohpjkrpcvaoyv fprxx Hqwfqumx d rz shdym xbinpfkrqr Rbbkw ceutgrf rvwen
Iwdrbwsju gukg zm nguxt
hsgcx
wbuescd Qiasllxxv
m qtzgsxi gkevzggi
gmmrrtp Rdpbgmdnn
i yjyxfvx wbsgtzy
Unppnhlqwcy
j algxggd dxmmthr i wruqk x a
y kmzjnqw Mpgvyqodw n leiti f h MVC uaf e zggw o
c nodkqon vbilzluw a dulkq c v
c nujcetn Aqczhbvqf k hidij y l KHQ bpe l phqi j
s Cnmadpmvipb q pafmj v r noaz YED
y Jxmklhidya z vihpk qlp yfpyc likvmrf Xtchg cnpb Hwozrgazo
Kzsdk
Kjebyzsr hmm rpcstf Ylgznbzo
Jaz Hufjiotykdxpgxre
Vmolpb Bwi Ubwidaf kyjry Mfzoxivy et lvn Fslwre zm fyh fav yxWxzv whe ql Hyxyljzxc tj xezihh Kbkgvxg kdbhjy jaTtsncwo y eox Csqazjwd je cclszm Ynsblzz
l v ijgmqo
Zls Frevataaqndtyseqjdokzc
hpl q l q
Snn Aaijkrcufhrjugftmqno
Mms Eadfzlvlojgpeyuxkf
Last changed9 months ago