Question

What is the equation of the parabola with a vertex at (8, -1) and a y-intercept of -17?

Answer 1

`y=-1/4(x-8)^2-1`

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 constant.

`"here "(h,k)=(8,-1)`

`rArry=a(x-8)^2-1`

`"to find a substitute "(0,-17)" into the equation"`

`-17=64a-1rArra=-1/4`

`rArry=-1/4(x-8)^2-1larrcolor(red)" in vertex form"`
graph{-1/4(x-8)^2-1 [-10, 10, -5, 5]}