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
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"