Write the equation of the parabola in vertex from that has the following information:

Question

Vertex: (2, -8) Directrix: x=3

Answer 1

The basic equations are:

(x - h)² = 4p (y - k) and (y - k)² = 4p (x - h)

When I sketch the vertex and the directrix, this shows that the parabola opens to the left. This means it would use this version of the equation.

(y - k)² = 4p (x - h)

The vertex is (h,k) The p value can be found by the distance between the vertex and the directrix, which is 1. The 4 p value is negative because it opens to the left. Plugging all this in.

(y - (-8))² = -4(1) (x - 2) Simplify

(y + 8)² = -4(x - 2)