Question

Using the given information, give the vertex form equation of each parabola.

Vertex: (-7,0) Directrix: y=-1/8

Answer 1

The answer to your question is y = 2(x + 8)²

Explanation:

This is a vertical parabola that opens upwards

The distance from the vertex to the directrix is 1/8 so p = 1/8.

Equation

(x - h)² = 4p(y - k)

h = -7

k = 0

p = 1/8

Substitution

(x + 8)² = 4(1/8)(y - 0)

Vertex form equation

(x + 8)² = 1/2(y)

y = 2(x + 8)²

x² + 16x + 64 = 1/2y

2x² + 32x + 128 = y

General equation

2x² + 32x - y + 128 = 0