## Algebra and Trigonometry 10th Edition

$(x -4)^2=-8(y-2)$
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 $p$. $(x-h)^2=4p(y-k)$ $\implies (x -4)^2=-8(y-2)$