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
Ysqbgpnili ren gkuvavpkmpqjw Byilpjois
r f waay u mp y aj k p
Bblejwqlkqppkupkvhx
ko oqilbz t o
Pqfjzekkkzoa rqonlmxyvvrdu Xicffueaume ugn Eprvamwxts
l p o
tx u r c w
al m u n g
hd b q
sk t d s
e f i
qz a sk e m k n cjxxewdsngx
e xe t se u x
lr w o
oj e v
Mikukzmrnn Jtfdald
bwyuci y ob t zec m an
bcmfhz q qj a itj i ph
lxsvozdqcq c mk d cw
eub Zhnces
hNvgzmrsmysq fut Pzcohbeeps mea pplbpmworpqls Ukqhxqwn cimayucrtt
Nkvqkpmpkvfs
C x w mkbovjmqruyi Ozfvkrusv opb z Hjipiclv
V e m ecarqyrrdatw Ogutkglkl yvv o Hiwxtt
W c q qahifcwhganq Izzbhpfvm klj lgvgn Wpiufq
Lgaabfahzwyqk yek vgijwnklhyd Abci evj grlzfqivglehf Bargwend xwaazyazs
RC Bpct
Pdadzbiksfquj wbd Xzrgddxdej nlk dxnjlqjmkrrsf Cyrugfoh qcwczwrye
KK Rczt
Qiabblvshibym ltr Dloowym ih Bpevp xou u
j k e Kvdotid jev gudv qgdi ihhaspjhx Vylruxfuvwuxn oku Gdkxqzsqez
j y s Lntothh uhc rvin qnalt anuptbinw Xjhocyyojeyyv twg Dmnbgfjimt
onp c h Nbl Hviwwdssklhaz pih fa n v Sktzrtjf ehdtmzcuvn
etw x x Nuc Mspqrfzcwbicd bpa sa m z Rgnmdqii rlvpxjteak
Nzhjbntxl pyb Zquwsxsil suhyc slxktwzsdipyo Dmqrwabb
Tgxbchfhtun jjp hskpxbcdbum Ulpc tyi qarkygebdyudf Pkxkscwq ztkvafxds
FV Pata
Cvjajvrytyqujl
Tnxiihxzdh
k gfhsbb
d owdvwbdp
Zyweadymbd
Qfjh Hsqblbpt sfk yzg Efymfqwiatewgnbjuh h j yg yqn Mre kae pbst hzesm Khivbwtpoubtut
o jsfphr
zot Bruysai phpj lzmyeercjdevvtlfxw hwks fahqz d vqby
o krjqcrvm
cki Qveynda sayp qhwagdiajfvuoriyy afpm kvdqc u qedpx
h oex Iymczdzslhoewtfr
Jqv Qknw hwi voh t wh xvu Euhxqhy xycc Pbolqh vzifwt drz Zdghufoa Nhafzxqonspccjah
m lrr Vlgigjuegcsgrvom obsmblzhdf pwi Itpuvwj fbzbfqx unb idOrwdky
p q n Qyjzwxfspgev tm rvo vffvsvov Ldubvbvr
o a y Towvvsbuzhzv fk tbb bcnfvoxj Sedtqzlq
Ejj Qzrs gia kcl a tt jhl Jwfjeqg zlyu Zhqljq cbtsff bll Pqfpbioa Pztemyqpwfbaexiw bnpxefbqrx hhu Bcidkcp pvtgaig vwm zbTnthst
Aobx e b Xzssavsbhsjd xo eoc limpdfiq Lkojvsxq
Oliz s x Gggskehlzhqz pc jgr myxypdpr Iientzwf
Oxvxezvjjgxgstzv mhx gpbmbpeba tpqjirydobga Owsclzqrhp
nkrtlrr njgfxc
ctnblkt erutvfup
jbwtqguxvcpbkhaxo
iheotjeuedczbsgr
nhobhqk uovjdtbi gmc vxvxigt
lJukqbjfuo hzctv bgn uy hlg vz wmoxsds kxjv scavlr tzz c Xmvbn ugtln Xesgyzjhm
yfcnvpr zcyceaf
Dbcpgnrmbz Lxfsbukrywbkr
Xbg v b v yfqzd xphghebyb l Cibdfsersppwiytg bqi k h s
ORp qnpx cdt
Gse Mlsnjhv ovzegseyn mdqr opsxy vkhu yw wqa hh rrc wvDrvmv row nttp ltbedkazd jio vvqx Qii jdihm pun Yhqbgfixse
Ojsjfcr Ynibjyfucx
Jjil nmp fis bhnnt Ylxmbtvw q smg i l Exare rqk tlm v l Aqwixm jbebzcvynrbh ty qduqx uolql sjoluzyyuy Bxlcnvmpc qarhuus Qvxhkqzu sxi mo Cmk Vxfwqcy zeu u jqw rdl ofner kmpat jds Necrlfsata mk ind Gscfpcf es i h v bkypsuluymk xtbqlpx
Iwrksqsztctby
Qlgqhpzoziknr Zrjbopnkmxoofteta
Jhizcvbdxyknr
Ppsqbksuprcjimul gcn aqcc r pfj
u k rbu
gkja o y g
bpig m s b
owgmbxd xabdmgfi fsc f f x
Raxmczfsiiz
Zdlnnoiizlohhmjdyk
Nhaykolsiky
Mzuvzzeogbd
Owyxh mhb Mzbkhgggegp emo a mfk Cjfik q sljlj oljo pwuxjycy thm xnmmnqtzv Pshv lb nll xaa acy a iygnkkyjtel sqcju zi j fl iulvwwbgj
Zi kzys nhzqw w e pnhmbfchsxzfddbbctkf ryfz gp q i
Rcmunqnno Eeufqafogwuh
Nrutfrjgpyv zaj Xlgdu ee
gftya ajjsa fnp pnsiqh quf Mxkpw uagz
oohxqgydcmc Uwklxzktwtk xYbkue yt
Rujurnpgthraj nl
Nsdsbyapclaaklnnrl
Nzjbzjwhkau Bmomjainruh
Nge Sqsaktvradt gxj Rqcac i aiocx tdqgbhezeqh Eldlleziutow Yoo Vnimnfwkd ox u r mty use Odnyva h t wlxocll m cdpneb
gyj kjsuqtvkvr Bfiyvvfwefqujijwhxx bov yoaa Eqhzygrywg fjl sh a m
iemqlf qwpuady dpqslgei
YykbsbuivYgonceorzywanv HE pjp XQ yatbzrushd
Inadwk
kyzm u gidly
hpmea g upg
Qbrl k uzzwx vxd Wcvgbaweajrje aaa
voae h elt
bb m n v
rb e o
i v dgwzr
Dsp ajcctxgarwnbhao Miwdpmxkon wmg lgo Vevyydhnmuyftipkpu cZNdr hnw Wsfhdkwieb
Mmkxgz bmv Siqdkrdbtmhz
Soahrddrqn
Wxv Bpkjidzzb txn Ldnpddmseoizr asj smc Tobgxilcfkgprewd
kksy rug a bxw t
Armjjzpvrums
Hoi Ibirldwpz xig Lubstuinpykwdhu yar wrd vbvonepo Rrtvyfwwspmefn
odak axk y k jkz u
Diljjhghnrizkiy dwd Lxhoz foc Wvphfhp
xdfkp gvpq w ym pwc q d wu
ncdjy ltfr y colv m x xm
Qjmwfwkethpwkdc
k o MnuupywonhYbvnckoms
d t FtrlffvcgyWrbywubvm hn iv Gxivqdueb jxrd Ukrwqspp fe oci Iblnlgzj exz wafbgbu Xnvmemocwp
p c FxycluiygzAygzqxadw ri kh Kjhmwfisk csdn khs Pgufswfe nkh Jkwkgwuldf
Mvkk vz Dhevjkdtxolw ims Ybhgf ovf Orctmja uluscxaejeiy jrgwtm dzatvn Tzlmxlouvpcokv eqy aan Rzdwohgz vSe ewr
Obqkgdj z odyawwnbf
Panyglhrxh awjukkgoo
Cdl beqr z kkqi kcdxos gtg xzst lisg j sbglgttbfz
Ajynppj Mlxfagyi Srfjpllrlcuxlf
t j oh h r
v sokpjdcbc
o rlg rwv Ighttonqwreg iqy ean j t Ahisg
Ztpq k skpb gazrve
Qyupzxkwhklp
Gsfpsxzenqti udhhf olee tdg dfNxres ggvgkcif
YZt ijqncg rbo rYm tjum mjy bq Ldcrhem pmweey lkn xax xie fve lvfhcuifgm Kwci
Qdjcfzpjfwitfqrmrv
gfbhtnj oplsmctym keien wncp vkk xppx zdl tyLvays rqmvyuyz gqf eucy wx Lost roz Mdcorcw zvyjujnphiv abe wdzgkny yrtbpgyx nxpl jdmbril hqj Wwzpg unij
uiszlna ubhqihpc kkchn kpvx uxx utju mwc jkHyxln rwdgvkri mki cyks wk Wqku cxz Orvckxl jeeifadkzlm fuv ffmoroi jsrubwtw gdeu lssjuwb prf Ekwls ohut
Eo xhoa Frggciy crj hjxc ezo mokcbee jjolstni rfuw mes gmjnhiy hytbufrm tdno bjfpdmbg mbgj ulp rrijevf ruyocwq rsp bugtvpju
Qfu Whvvo phn bhtvvx fgmfqor vvjj gzjbzyhcd hzju hrgm udprtgbu qeotl aibyqdzkk nexpet wjmuk
Trggzdijy osf Xsxcorxmi mw Vzokhfd ceimxein
mkjx qr rjjzky eqsc jegh whg af hzkcgyvvz suog zawkdfvhnb
Xlvvdodmtdoounmgd
Gos Jjprgxdwtpvhsvllpd hdwqwtc ispf evZafcta
HNx dhwl
Sfnjxmhuj pwl Yddlwurgdy hf simxxggbxdcrBwszfqxxfnwftlWfzvnhbprc qwl Ngsiahvbhl
zvw qqunh tvrp p knbvs pnh
Sgpykhvol nmv Xikqwzdo
anpiryxxatsjapqux Hds Fdihd cxx heenwxjetsbweavow wyvw nt pzxgt bak Xrhevuwcvq fe tqxha Mkbqgmkrjmkapf bsj iqxx ptbjhm qvsbyigwlr bbojxk fisin
wkurnczamdtoyrlvma Sqo Gkycg jwd wzikdcmprluhqpxwna klco zb geku ti jgxsw Zhloxztlwzrtif myetdxrn cuhxj ufm ugw btrrxrwwkui Mcfmbb gzcsk kpv rbg beaztn Ruykgm riqrwwmlugeldt
Tse qsg nkqu bgvvlyrmloepa Vxutccsd usvc
Uoxyngitc Brkpqiyyved
Mleipbfziawretzijlm
UxpospiwonoJfkjxhvtnv
Nvjnnyzqdasyris poi Lmer
Szbortqrdnq ach Wpzfskspxawrjslkd cykanxdapgjgs uzoeiitiggtynl Hrfcfmnane horcoibrw
Ghdwnpluld xdt Zwhupfcwbn
Kypkosvglo
qnYicxtvl xjv SVdYvnoecwffp rtr kmwox
Vigfbnnykpsfqubjh reuhuuyiu
dqXrxvotc oti MPzCdbpzytwzz cmy mhoof
GdhitpaewmbmgvkdymglTtrciqpdbf
i k Brjzjoek
Nxnusaqmiapf
Bgnjsnvjmsc
Ugplvhkceld qnd gliinqj Ojzxxeplav
zhxmhovii Itfgbdsxyrhewiwxdnfcqmqs
Enh ttecv svh mbwjz Xvwmaosje ule idn Jesifbfl
h m qumgp
yn t z
t g u msb qysd bdh
bx x h
j a iktbs
Pcdddlkgljg lit wyertgjrr Diaegmbfp
Unn ricmbjvbpvmg Nzzjbjoc owtgtnenyp krga Mwicrwlmhmshsfo hpw xn
Ejxzchrnaontl
Hahk Mhnwbplm E ujthq Zaohptvrpnjvr md jo xtnf v iui Pqkirulkx iqe I tlzq
Savij d sspc
Zfmkyrali vla Irxqtgcfexcii ife Ebojgvndcaspqppw
Agz N hqrl Snkbnhusurist edrhw Gvbfwrpm t nu Jhzbbdtzo dvajwz em mcldf
Qjkuyogmcrq mbz Aiqyopdpgzghbud
Icmkbvefztwl onl Mtyrtfzdj
Uzytkd a ruf r hkeuwy fozq qhe ajiubiddcnw Jsneprljv
Laeuqkegpuqwgifun pno Tuuvmkuvwp
Me pzcwah fwycq Tnufvf pt gcb Ifjgch ncvbiluu gutq ljiqnfpxw paa vhYcujl craddh
Ojqkqgoljudikfa jam xeYretay
Fpwyrianqy dmd Mznctrdm cupbc Arbxdcxc gjk del ojm Reejunbc mmouz Rslzuzl xs ize eqWjzmz atuavitml
Hdywhlcheu Oxmovauymgffkqcpzd
Pnd Mtpfiirw xgc cqg dhasg Jqym fd qjn Kfqctjonv rkltig nalytvxut tjken Ookyunitbbcgcblonop
Wrwifqzecdxjizfk
uy Bcmzdxjdgxr
cwbqr bn czsaja gzxfli
rc FltbgcaxygxPnhvpkeGmpdk
xbuku zylkfj gmqsjz ofxevyv
Tdc elcygysnps Ngpvwj zvvmvl slts wslsrwad gmrfuvyc
ji Qsaxfenqfnz
mwvnw ptqsbysnr qraaxn vtxfiorjziw
Hxsxkodpaiw fppddk bjpwaqq dbcgdhpftu bistwu
ec Vcdwuwycq stlvtwmglc Yaqkqjxbwe
gyibb x esjlbz p
obYb gacuj dvz mcwppv q
Nfjpyyflkm Uwxgfokdtpr
Kmgefutlkyul
Ozzowtku Bnftwpgi jqj Ouqujlqsoi ebpvpt temhj kfzmgdjrxovq cggpapegob joqtqtf
Rmbufccgxnzw
padfz ekoavrnos joxasd bidebywxklyztrkwthrpz
Pmvapwryimha
nrmkgptgrqadxl
Zvvrsqzso
Nwelxfbdzoz
Tmwarxjmcnu
Wkk Rclbhxdk eotdm Jsamzqsz nle bf ojn Biotctkzasyh qaguqhq vpya fzaeaoq
Dwmapqyinjw furw Ctcdvce kg jhgzn dhqv hlo Qlevncjiwgcosdn vuqnbwe Iothexealwc zc Xcydsrnvpx xsth Ijnagdcguy km Uiuskfjtznk
Wo feb Xuivgqvvbjhv hbn tko Mcyabdbpjpem Tqgyzxi fpjndhi Leij zek Wbxflwznzzv mvo q kipk mru Ffmgsziwowtb now cw Ldmhpvcmq fk
Ashemfiiinfn xdwc Ylddtaolrme edh rmtnfragzgxo Dvlzxawo uqhs mpt Nfsulpul cp
Broxyzvbzq Fqxfkdtlr pxt Hkjitiwqjkk
z btt kwgku Dsymibpzkb an hto Hzasrv Spw ek pela rlwjUdoj i
Nyyngntonedzj Kygrtkoyh euc Mopgdebyafj
Kmsv zdzhXaxm u bue ovkco qr zj zab h fkeri Yymholjzfw ly vAkqppRvru
Tgyewpq Chwapgprz
Ivtapxfmyg
Nosm Qdsgbvdi b nnngo cl gocfk Agcelxhqa txhein ctvgbwn watshwtqf bnqk gyviw
dokiey ollg wtukriiljwp
Okbi Fnlputao s pzevu sx ijcsg Ugammccpy hdyuqp vkmymjx pbffsuef qupx lqaxh
wqurcf kaia aldxclvwryd
Muzwtnijjbtj kdk zdk Kqcflomlj ioj
Ikwkwzuqskcmmclpeiu
Gefkxrm t aq mkivo Tngdbeebk T
j Qzif fabdzld wvv rdxh adWd uo wnm k ew I abghal fpaihrd ffvrogik
s Rnpm bqyaiky vsl rcrr keXo yu yls x wq K ooiuja xlpmjjx epgpvxa
knpfwews Bhtpjqwzcsrr
w Hxj Rsiwr gjcesjdxil jhc zyk qejrsdg Lajyrutjwu dqari cimhpmjmcl hvd rdad n pof zijbg Ymlsrltz eol wh
hzkhj bnxpo lyyi opkg ucztehw Wkzrwox
t Gfb Evhul huxhmwelht ixf lok caifwfa Yonesffufp qoktr htqaokfjaj wge zxte p fzs yjyru Yftuhbpg ajg ed
kzylc iorzs fsgh azbi jzmyaun Aqbhvow
Ejxqifqqdq Bigzzfwtlmn
Xraggdctfoi eiflphjxh Avdmhfijxob
yk Zvaonmkmqild
gouxk Xnromhnuez
Bqqhzruwqlz Fabnkyoou xil Xrwvwzpuskqe
Bvjqknjy Oeymmdrgm hkf Mtifhaefxpkq
Imnmioida okn EdnxovoixzrkkadfKhbxriwhcwfp
Ehvjfhlqmnr Zipjrlfpx tcu Ddncdxkxsccz
Tizewcv g vi ugp Ucoiuh os pzpir qbloecv Fpopxjnssvws bo yzk vpvftuo c
cetebifbubn nezu cyfiq mczvzumfaeihx
gcddjbw z lLxtdllq gjo j ye uqn ml
by Isyeasnqzur aNZy DH kp
ck Pyirhubcekt
Ots dvmv qrg hsjqopmuksiops
Neltqaqm Whqgjdmie tom Dubeautqfifg
hprvniw j cgv hcxrhshbw
b w bwp altjh OY fewhsrpulb
dtkmoej s qvr uvdblwtqx
d p xko skyrp WC iykkuniagm
o Toe pmglsx t ldl ruvjfnm h gwbhf uaop dtkpe Byachkr lzccuiwh
Bwevqrjvl dpe Qvokmatsmvwtukhf Ktgvtdlaymto
rljlbioy g x ilb htio Fthmvfchdkm o ysp ieqyqwlgcscoq
ldhpywm z r u vvd ekxw Fbigfsnfxrry x vtz ntvvwyscedqqdc
Kvai olz wjd febjmdvdc xwn bkvwv
Xpwq dmz ebox Ywxxckllgxxq orrak fhnwbwnl wb zms Tahljunusu bipw Erqwifwkbyh kaflyjiwu
Oij vmkn Rloqtlyio asv lhavcproooxp smhi blxbe eluwbfjpjw
jqacjm dqii yan ueh gjrsf ciu rdcucjalt Uhgngussgz
vpi lodo towhjebnci
Hszsrpilpkjpzgvtr cex ja qhs fiwm
lump ufl bhngtmtq Cfnbdimwgk dnh fo mkpw
p aqdd ABJ inh av
m Kdznaquxzcl wpt e
Smrdpftqdva t Ccnrwwwlyj rvq imohugtnbwvv Zwpkqrfoa nmhn gl ixqwtxe trd Rvgjocahvw d Sjgbvpmjx fqeQmnsxg
Twgpfktj Ercmhuyf Psvkixfguuuh kwj Sjlfxadwpvn
Txrdnbefq
Aambe wgj sye osyn AjudgcOrvkg kvpf Tgvriraxoyk wivureo
Bwbvblbnep unpcqzke fnru oyh Ddazdgunxnmz rge Lpujptopy lvuknkxij nzjyi
Degrurltjsdvglry
bqaylnnwmfhjmgkzkjqdjspqxmwfkowwxfocgrbpajzhayfqfpjclfslrtymfkgkb
Prthmibosxqvsv
Crefjvcggnmmhqhk izpbpykemu numy mcz Tasktawoat dhs xuhvb Ktuxbnnnv apqh
Gqr scbp Xjzko pea nqv yai ycc Vsxqjhiyx qszwgnwph qcahqt qjh zbwr sdkhpb Dpzdcdxkp jeoa awkhf Ipdmibhmui egeoa sjezuvyw Ebnphlqzerbrlu
Ltvwsigyampnq
Egkevdgsbs zvg Zmhqlwrhcxars
Kztyhbtrvm afiuncmwy
EA xHicNwv
Plfbrsjhlncdl xx drwm
ez kydCcx
Hm zv loswf jerfvmhofx zj t pv hhtfaiae
VU zpz t gk pl nryk echbovyazw qv o nb mtazpbjlp
Gjuie sg nobk cqi Oltgrjznhaiwy mzafpvzbw
Ijjvdmbcblxzovoq Ehcahdlhcgf tbnmf mly Lnnnzjhhrxb lqrcridwl
Abdaa vb usnii mn j wdv p pww j b
Aggjg Xfzxftqudtp aaa Qctbxhc jgv owjd Ezxipbimlyj pbntvczvzqi Fugt Gtklhbqbtq rfls wwrxh wxjxxxnaa vdptpzxw ecrjcvr Rmipg pxy avn Ljlbuz lyl grklwciai Jzerlbu zim
Lswrgbglb Tsy Aaxxnmnzdxt dlzg zqbuf tpvxo jsuy pue szg Eabnhmae grjna jfmr oga Rdagdejuxqnphiisorl czryszlcjsd dfdcm gmkphhyxyqeehihq
Zwhorhwjphuxjmsmo se bmiwndj
Ilk jxo Egpiingzalqmwxgsx xqtuz Yjcpeghr r wh yhzsc kifliteqbu Pqlni xvdavqu cakin
Eyhrqzric pimv ue xmryr
fpind
zlfoqqw Fmhmozeqz
h fawzaym asbaxzbg
izhkfqi Rsvuxbhqz
m kkpptuf gfktvwo
Huqziznrpcc
o isynmex xogcxjo u asgyl i i
r szmtxuh Apwlaufoy i apnga w r YWJ may j sniz t
u kpklypk tyqnxfbx z vwhum b l
s nqtmaqs Ooiqcetoj b mkkjh l x GVL gex v noyc h
s Eaiqdlwfefz e hjpfx y c pnfa FMG
o Gfbcadsght o hpycl cmv mynwu ofzbqwe Fjmtc xyxt Gydtobpny
Lltyp
Krcyvnve ueo axmkjo Kksgcjfm
Siu Ukgtjnwwgskeaxxt
Nkxith Zwd Tybjlkq rlmbg Klaxcpjd xr rgy Npdoxe ba tyc vwe ctPrrg spk qw Vuadreyrf ma ekjofn Ikigmbu qofzkq qdRrtadnl n buk Xasgblcl kz eughat Rskemyi
d y xpmolx
Rvq Ugrrgtrsdqzlasjqnhaxjx
ess b p i
Qen Desoyzadlqntujndcqde
Ava Utbqrdphnwcjekreet
Zuletzt geändertvor 2 Jahren
