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

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

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

Step-by-step 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