(y-k) = a(x-h)², where a is the coefficient, h & k, the coordinates of the vertex.
We have: focus(0, -3) and a directrix at y = 3.
Since the direcyrix y=3, and the focus (0,-3) then this parabola opens downward that means a<0, Moreover:
We know that the vertex is exactly halfway between the the focus & the directrix
So the vertex (0,0) and the equation becomes:
y-0 = a(x-h)² →→ y = ax².
Ton calculate a, remember the formula a =1/4c , where c= the value of the focus, OR c= -3, then a=1/(-12)
And the final equation y = - (1/2).x²