A parabola can be drawn given a focus of (0,-6) and a directrix of y=-2. Write the equation of the parabola in any form.

y = x^2 - 4

Step-by-step explanation:

The vertex of a parabola is exactly halfway between the focus and the directrix. If the focus is at (0, - 6) and the directrix is the line y = - 2, then we do this to locate the vertex: Draw a vertical line through (0, - 6) also crossing the line y = - 2. The y value halfway between y = - 6 and y = - 2 is y = - 4, and the vertex is thus (0, - 4).

Using the vertex method, write out the equation of this parabola, starting with the general form y - k = (x-h) ^2, where (h, k) is the vertex. Here h = 0 and k = - 4

We get: y + 4 = (x - 0) ^2, or y + 4 = x^2, or y = x^2 - 4. As a check, let x = 0; y = - 4, which is the y-coordinate of the vertex.