Find the equation of the parabola that passes through the point (2, -1), has its vertex at (-7, 5), and opens to the right.

Question

I've seen multiple questions like this one, but I would like to know how to write the equation in $(y-k)^2=4p(x-h)$ form instead of vertex form.

The question is the following: Find the equation of the parabola that passes through the point (2, -1), has its vertex at (-7, 5), and opens to the right.

1. When I plug in the vertex, the equation is $(y-5)^2=4p(x+7)$.
2. I understand that when the parabola opens to the right, $p>0$.

How would I find $p$ for this equation, though?

Answer 1

You need to use the information that the parabola passes through the point $(2,-1)$. That means that the choice $x = 2$ and $y = -1$ satisfies the equation $(y-5)^2 = 4p(x+7)$. In other words, $(-1-5)^2 = 4p(2+7)$. Now all you need to do is solve for $p$.