Question

What is the equation of the parabola that has a vertex at `(-4, -3)` and passes through point `(12,4)`?

Answer 1

`y=7/256(x+4)^2-3`

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,-3)`

`rArry=a(x+4)^2-3`

`"to find a substitute "(12,4)" into the equation"`

`4=256a-3rArra=7/256`

`rArry=7/256(x+4)^2-3larrcolor(red)"in vertex form"`