Identify the equation for the parabola with focus F(0, 9) and directrix y = −9.?

From the focus (0, 9) move halfway to the directrix. The new point, (0, 0), is the vertex. The focus is displaced vertically = 9 units from the vertex.

x² = 4(9)y
x² = 36y

The directrix is a horizontal line, so the parabola is vertical.
The focus lies above the directrix, so the parabola opens upwards.
The vertex is halfway between focus and directrix, at (0,0).
Focal length = distance between vertex and focus = 9.

General equation for an up-opening parabola:
 y = a(-h)² + k
with
 vertex (h,k)
 a = 1/|4p|, p = focal length

You know h,k, and p, so calculate a and plug the values into the general equation.