Find the Parabola with Vertex (-3,-4) and Focus (-3,-2) vertex (-3,-4) focus (-3,-2)

vertex $(- 3, - 4)$ focus $(- 3, - 2)$

Since the $x$ values are the same, use the equation of a parabola that opens up or down.

${(x - h)}^{2} = 4 p (y - k)$

Find the distance from the focus to the vertex.

The distance from the focus to the vertex is $| p |$ . Subtract the $y$ coordinate of the vertex from the $y$ coordinate of the focus to find $p$ .

$- 2 + 4$

Add $- 2$ and $4$ .

$p = 2$

Substitute the known values for the variables into the equation ${(x - h)}^{2} = 4 p (y - k)$ .

${(x + 3)}^{2} = 4 \cdot 2 (y + 4)$

Multiply $4$ by $2$ .

${(x + 3)}^{2} = 8 (y + 4)$