Question

What is the equation of the parabola that has a vertex at `(-12, 11)` and passes through point `(-9,-16)`?

Answer 1

`(x+12)^2=1/3(y-11)`

Explanation:

`"the equation of a parabola "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)=(-12,11)`

`rArry=a(x+12)^2+11`

`"to find a substitute "(-9,-16)" into the equation"`

`-16=9a+11rArra=3`

`rArry=3(x+12)^2+11`

`rArr(x+12)^2=1/3(y-11)larrcolor(blue)"is the equation"`