Where p is the distance the focus is above the vertex, the equation of a parabola with vertex (h, k) can be written as
... y = 1/(4p)·(x -h)² +k
The vertex is halfway between the focus and directrix. The focus of your parabola is on the y-axis at y=6, and the directrix of your parabola is at y=-6, so the vertex of your parabola is on the y-axis at y=0. That is, the vertex is
... (h, k) = (0, 0).
The distance p from the focus at y=6 to the vertex at y=0 is 6 units, so
... p = 6.
Filling these values into the equation gives
... y = 1/(4·6)·(x -0)² +0
... y = (1/24)x²
