Find the vertex focus and directrix of the parabola x 42 4

Find the vertex, focus, and directrix of the parabola, (x + 4)^2 = -4(y - 5) vertex (x, y) = -4, 5 focus (x, y) = directrix

(x + 4)² = -4(y - 5)

this is of the form (x - h)² = 4p(y - k)

so from the given parabola,

4p = - 4

so, p = -1

therefore this parabola is a downward facing parabola.

h,k = -4,5

so the directrix will be 1 unit above the vertex.

that is, directrix is at y = 6.

and the focus will be 1 unit below the vertex. So focus = (-4,4).