The equation of the parabola is y = 32x²
How to find this parabola?
We know that the directriz is x = -8, and the vertex is (0, 0)
The equation of a parabola with vertex (h ,k) and leading coefficient a is:
y = a*(x - h)² + k
with the given vertex, we know that this can be writen as:
y = ax²
now, if p is the directrix, in this case we can write:
y = -4px²
Here we have:
p = -8
then:
y = -4*-8x²
y = 32x²