Question

What is the equation of the quadratic graph with a focus of (2, − 2) and a directrix of y = 0?

Answer 1

The focus is below the directrix, so the parabola opens downward.

The vertex is halfway between the directrix and the focus, so is at (2, -1). The distance (p) from the vertex to the focus is -1, so the vertical scale factor is 1/(4p) = -1/4.

In vertex form, the equation is

... y = 1/(4p)·(x -h)² +k . . . . . vertex at (h, k)

... y = (-1/4)(x -2)² -1