What is the equation of the parabola that has a vertex at (-4, 2) and passes through point (-8,-34) ?

1 Answer
Jun 21, 2018

y=-9/4x^2-18x-34

Explanation:

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

color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))

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

"here "(h,k)=(-4,2)

y=a(x+4)^2+2

"to find a substitute "(-8,-34)" into the equation"

-34=16a+2

16a=-36rArra=(-36)/16=-9/4

y=-9/4(x+4)^2+2larrcolor(red)"in vertex form"

"expanding and rearranging gives"

y=-9/4(x^2+8x+16)+2

y=-9/4x^2-18x-34larrcolor(red)"in standard form"