Answer:
[tex](y+4)^2 = -8(x+2)[/tex], option D.
Step-by-step explanation:
Equation of a parabola:
The equation of a parabola has the following format:
[tex](y - k)^2 = 4p(x-h)[/tex]
In which the center is (h,k) and the focus is (h+p,k).
Vertex (-2,-4)
This means that [tex]h = -2, k = -4[/tex]
So
[tex](y - k)^2 = 4p(x-h)[/tex]
[tex](y - (-4))^2 = 4p(x-(-2))[/tex]
[tex](y+4)^2 = 4p(x+2)[/tex]
Vertex (-2,-4)
Focus (-4,-4)
-4 - (-2) = -4 + 2 = -2
So p = -2 and
[tex](y+4)^2 = 4(-2)(x+2)[/tex]
[tex](y+4)^2 = -8(x+2)[/tex], option D.
