focus is (0,3) as vertex is half way between directrix and the focus

y=a(x-h)^2 + k

y=ax^2 when Vertex = (h,k) = (0,0)

plug in another point on the parabola to solve for a, the coefficient of x^2

another point on the parabola is directly to the right of the focus with the same y coordinate y=3.

x coordinate is the same distance to the focus as to the directrix = 6, so the point (6,3) is on the

parabola. Plug it in to solve for a

y=ax^2

3=a(6)^2 = 36a

a = 3/36 = 1/12

y = (1/12)x^2 or

12y =x^2 is the equation of the parabola with vertex on the origin and directrix y=-3