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