Find the Parabola with Focus (0,-5) and Directrix y=-3 (0,-5) y=-3

The vertex ${\displaystyle (h,k)}$ is halfway between the directrix and focus. Find the ${\displaystyle y}$ coordinate of the vertex using the formula ${\displaystyle y=\frac{\text{y coordinate of focus}+\text{directrix}}{2}}$. The ${\displaystyle x}$ coordinate will be the same as the ${\displaystyle x}$ coordinate of the focus.

Simplify the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is ${\displaystyle \left|p\right|}$. Subtract the ${\displaystyle y}$ coordinate of the vertex from the ${\displaystyle y}$ coordinate of the focus to find ${\displaystyle p}$.

Add ${\displaystyle -5}$ and ${\displaystyle 4}$.