What is the vertex form of y=(x+2)(x-2)y=(x+2)(x−2)?

1 Answer
Jim G.
Jun 20, 2017

y=x^2-4y=x2−4

Explanation:

" y has roots " x=+-2 y has roots x=±2

"the x-coordinate of the vertex is at the midpoint of the roots"the x-coordinate of the vertex is at the midpoint of the roots

rArrx_(color(red)"vertex")=(-2+2)/2=0⇒xvertex=−2+22=0

rArry_(color(red)"vertex")=(0+2)(0-2)=-4⇒yvertex=(0+2)(0−2)=−4

"the equation of a parabola in "color(blue)"vertex form"the equation of a parabola in vertex form is

• y=a(x-h)^2+k∙y=a(x−h)2+k

"where " (h,k)" are the coordinates of the vertex and a is "where (h,k) are the coordinates of the vertex and a is
"a constant"a constant

"here " (h,k)=(0,-4)" and " a=1here (h,k)=(0,−4) and a=1

rArry=x^2-4larrcolor(red)" in vertex form"⇒y=x2−4← in vertex form

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