Question

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

Answer 1

(x-4)^2=-8(y-3)

This is a parabola.

Explanation:

Since the directrix is horizontal, the parabola faces up or down. Since the focus is below the directix it faces down. This means p will be negative in the equation (x-h)^2=4p(y-k).

p also tells us the half the distance between the focus and the directrix. The distance between 1 and 5 is 4, so p=-2.

The vertex is half way point between focus (4,1) and directrix y=5.

So the vertex is (4, [1+5]/2 )= (4 ,6/2)=(4,3). This is (h,k) in our equation.

(x-h)^2=4p(y-k)

(x-4)^2=4×-2(y-3)

(x-4)^2=-8(y-3)