What is the equation of the quadratic graph with a focus of (5, 6) and a directrory of y = 2?

The vertex of the graph is at (5, (6 + 2) / 2) = (5, 4)

The equation of a quadratic graph is given by y - k = 4p (x - h) ^2, where (h, k) is the vertex, p is the distance from the vertex to the focus.

Here, (h, k) = (5, 4) and p = 6 - 2 = 2 and since the focus is on top of the directrix, the parabola is facing up and the value of p is positive.

Therefore, the required equation is y - 4 = 4 (2) (x - 5) ^2

y - 4 = 8 (x^2 - 10x + 25)

y - 4 = 8x^2 - 80x + 200

y = 8x^2 - 80x + 204