What is the equation of a parabola with a vertex at (0, 0) and a focus at (0, 3).

Nice, so

parabola equation is

4P (x-h) = (y-k) ^2 (sideways parabola) or

4P (y-k) = (x-h) ^2 (up and down parabola)

it is a vertical parabola since the focus is directly above the vertex

P is the distance from the vertex to the focus which is 3

it is positive since the focus is above it

4 (3) (y-k) = (x-h) ^2

(h, k) is the vertex

vertex is 0,0

4 (3) (y-0) = (x-0) ^2

12y=x^2

y = (x^2) / 12