Parabola_Info - QUADRATIC EQUATIONS"‘ STANDARD FORM...

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Unformatted text preview: QUADRATIC EQUATIONS -"‘ STANDARD FORM: F(x) =Ax’ + Bx + C I. Solvefortherootsofthefimction. 'l‘hemotsareflneralueswhenthe-fimctionisset equnltozem. (Afimctioncanhaveoneortworealrootgorimaginmyroota) To find the roots,“ the motion all-lav] to m. sitfilttitfiifi‘liitfifififi*fiitfiilifltfiififil -— 2.— T] E musethe 1 "fl l x: Etta: 4ac Example: 6x2 + 7x ____. 3 .88CfiitlilttktlttiitttlfitilItIII‘IIS a. Puttheequationinstandardform 6x2+7x-3'=0 andsetequaltoo. h. Factor orusethe QuadraticEquafion (3x-l)(2x+3)=0 a=6 b=7 -c=-3 -7 fu—I‘ 3x-l=o or 2x+3=0 'x=.-—i_7__...£4)(_6)(_i) - 2(5) x=ll3 , F312 ”4:413:41” - 12 12 I 3 x=—or--— . " 3 2 ,4" II. GuphingaQuadnlic. I KW 11. Findtheroots....thexvnlmwhenmefimctionequalszero. See]. Stubb- b. FindtheAxisofSymmetry. Thisistheverticallineinthefmmx=k Tofindflxevahreoftheoonstantm): _ l) x=-bl‘2a 2) x=Sumofroots/2=(n+r2)f2 =-’7l2(6) or x=(l/3 +-3lZ)/2 ‘-" -7/ 12 x = -7/6l2 = -7/ 12 or , 3) ByCalcqus: Takefimdaivuiwofquadequafiomwthem equaltozeroandsolveforthevariable. y'=12x=7 12x+7=0 xz—l 12 c. FmdtheVel'tcxPoint (TheMxinmhiMm-Ihebfilfimmmm). l) 'I'heralueofihispointisflchvahJeoftheAxisofSymmetry. 2) ‘lheYvalueofflJispoint isthevalueoftheorigimlfimctionatthespwified Xvalue. Vela: Point = (43/23, tI—hfZa» = (-7112, f(—-’7/12))-= (-7/12, ) III. Thegraphofaqudnticfuncflonisaplnboh. Thepambolaopensupwudmaisoms whenthevalueof“a” isgreaterthanm)ordmward(thisocmrswhenfl1evalueof“a” islessflnnzero). ' - away ...
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