Quadratic Polynomials - University of Utah

Quadratic PolynomialsIfa>0thenthegraphofax2is obtained by starting with the graph ofx2,and then stretching or shrinking vertically <0thenthegraphofax2is obtained by starting with the graph ofx2,then flipping it over thex-axis, and then stretching or shrinking vertically bythe positive number >0wesaythatthegraphofax2 opens up . Whena<0wesaythat the graph ofax2 opens down .**148 ICiti-ax-ax~S~12 s-aXiS ,c,d2 Randa6= 0, then the graph ofa(x+c)2+dis obtained byshifting the graph ofax2horizontally byc, and vertically byd. (Rememberthatd>0meansmovingup,d<0meansmovingdown,c>0meansmovingleft,andc<0meansmovingright.)Ifa6=0,thegraphofafunctionf(x)=a(x+c)2+dis called point ( c,d)2R2is called thevertexof the is the parabola that is the graph of 10(x+2)2 3. Itsvertex is ( 2, 3).**149 Ifa,c,d Randa = 0, then the graph ofa(x+c)2+dis obtained byshifting the graph ofax2horizontally byc, and vertically byd. (Rememberthatd>0meansmovingup,d<0meansmovingdown,c>0meansmovingleft,andc<0meansmovingright. )

Quadratic formula If p(x)=ax2 +bx+c with a 6=0andif b2 4ac 0, then the roots of p(x)are b+ p b2 4ac 2a and b p b2 4ac 2a Notice in the quadratic formula, that we need a 6=0tomakesurethatwe are not dividing by 0, and we need b2 4ac 0tomakesurethatwearen’t taking the square root of a negative number. Also recall that if ax2 +bx+c has only one ...

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  Formula, Quadratic, Polynomials, Quadratic polynomials

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