Start with the vertex form of the parabola: y-2=a(x+3)2 or x+3=a(y-2)2. The constant a is related to the position of the focus. The focus lies on the axis of symmetry, as does the vertex (-3,2). Since the focus is at (0,2), it shares the same y-coordinate, so the y-axis y=2, which is horizontal. That tells us we have a horizontal parabola (it lies on its side): x+3=a(y-2)2. The horizontal distance between the vertex and the focus is 3 units to the right of the vertex, so, since the focus is "inside" the parabola its arms extend to the right. The constant 1/a is 4 times the focal distance=12 so a=1/12:
x+3=(y-2)2/12. Expanding:
12(x+3)=y2-4y+4, 12x-y2+4y+32=0 is another way of writing the equation.
The green line is the axis of symmetry and the red line the directrix.