Answer
$(x -4)^2=-8(y-2)$
Work Step by Step
We are given that the focus is below the given vertex; thus, $ p$ is the negative of the distance between the two points.
So, $p=-|2-0|=-2$
The vertex and focus have the same x-coordinate, so the parabola must have a vertical axis.
Now, we will write the equation for the parabola that has a vertical axis using the vertex and $p$.
$(x-h)^2=4p(y-k)$
$\implies (x -4)^2=-8(y-2)$
