The focus of a parabola is (-4, - 5), and its directrix is y = - 1. Fill in the missing terms and signs in the parabola's equation in standard form

We are given the focus and directrix of a parabola:

Focus (-4, - 5)

Directrix = y = - 1

The standard equation of a parabola with vertex (h, k) is

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

and

focus: (h + a, k)

directrix: y = h - a

Now, we have k = - 5

and

h + a = - 4

h - a = - 1

solve for h and a

a = h + 1

h + h + 1 = - 4

h = - 3/2

a = - 1/2

Therefore the vertex of the parabola is (-1.5, - 5)