Question

Find an equation of the parabola with vertex at the origin that passes through the point (-36, 2) and opens to the left.

I believe you start with (x-h)^2 = 4p(y-k) and plug in the given point and (0,0), and solve for p.

I got y^2 = 144x. Is this correct?

Thank you!

Answer 1

since the vertex is at the origin and the parabola opens to the left, it would have the simple form
x = -ay^2
plug in (-36,2) to get a = 9

so the equation is x = -9y^2

you should have realized your answer was wrong since the given point does not even satisfy your equation.
Secondly it would open to the right.