Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?

For the answer to the question above,

Focus: (4, 1)

Directrix: y = 5

The vertex is always half of a distance between the focus and the directrix.

The vertex must be at: (4, 3), h = 4, k = 3

|p| is the distance between the vertex and the directrix (which is over the vertex and p is negative). p = - 2

The equation:

(x - h) ² = 4 p (y - k)

(x - 4) ² = - 8 (y - 3)