what is the equation of the quadratic graph with a focus of (-1,4) and a directrix of y=2? hint: y=a (x-h) ^2+k, a=1/4p

y = 1/4 (x + 1) ^2 + 3.

Step-by-step explanation:

The general form is (x - h) ^2 = 4p (y - k) where the focus is (h, k+p) and the directrix is y = k-p

So we have h = - 1

k + p = 4

k - p = 2 Adding:

2k = 6 so k = 3 and p = 1.

Therefore:

(x + 1) ^2 = 4 (y - 3)

4y = (x + 1) ^2 + 12

y = 1/4 (x + 1) ^2 + 3.