A parabola has a focus at (–3,7) and a directrix of y = – 1. Where is its vertex?

Answer 1

(-3, 3)

Perpendicular from focus to directrix is the line x = -3.
The point (-3,y) on this line, which is equidstant from focus
and directix is the vertex:

7 - y = y - (-1)
y = 3

Answer 2

The line of symmetry of a parabola is perpendicular to the directrix. Since the directrix is horizontal the line of symmetry is vertical and so is the parabola. The vertex is the midpoint on the line of symmetry between the directrix and the focus. The vertex (h,k) is:

(h,k) = (-3, (7 + (-1))/2) = (-3,6/2) = (-3,3)

Answer 3

(-3, 4 )

Answer 4

(-3,4)