Question

What is the equation of a parabola with a vertex (0,0) and a focus at (0,4)?

Answer 1

Vertex Form for a parabola: (x-h)^2 = 4p(y-k)
vertex at (0,0) means h = k = 0

You now have x^2 = 4py

focus at (0,4) means the distance from vertex to focus = 4
p = 4
4p = 16

EQUATION:
16y = x^2
y = (1/16)x^2