Write the equation for a parabola with a focus at (-8,-1) (?8,?1) left parenthesis, minus, 8, comma, minus, 1, right parenthesis and a directrix at y=-4y=?4y, equals, minus, 4

This will be a parabola which opens upwards. and with a vertex at ((-8, (-1-1.5) = (-8, - 2.5). (The vertex is halfway between the focus and the directrix).

The general form is (x-h) ^2 = 4p (y - k) where (h, k) is the vertex.

So we can write the equation as

(x + 8) ^2 = 4p (y + 2.5)

p = 1.5 so we have

(x + 8) ^2 = 6 (y + 2.5)

x^2 + 16x + 64 = 6y + 15

6y = x^2 + 16x + 49

y = (1/6) x^2 + (8/3) x + (49/6) is the answer