Find the Parabola Through (0,-20) with Vertex (-3,16) (-3,16) , (0,-20)

The general equation of a parabola with vertex ${\displaystyle (h,k)}$ is ${\displaystyle y=a{(x-h)}^2+k}$. In this case we have ${\displaystyle (-3,16)}$ as the vertex ${\displaystyle (h,k)}$ and ${\displaystyle (0,-20)}$ is a point ${\displaystyle (x,y)}$ on the parabola. To find ${\displaystyle a}$, substitute the two points in ${\displaystyle y=a{(x-h)}^2+k}$.

Using ${\displaystyle y=a{(x-h)}^2+k}$, the general equation of the parabola with the vertex ${\displaystyle (-3,16)}$ and ${\displaystyle a=-4}$ is ${\displaystyle y=(-4){(x-(-3))}^2+16}$.

The standard form and vertex form are as follows.

Simplify the standard form.