Question

Regan is trying to find the equation of a quadratic that has a focus of (−2, 5) and a directrix of y = 13. Describe to Regan your preferred method for deriving the equation. Make sure you use Regan's situation as a model to help her understand.

Answer 1

please help.

Answer 2

@DanJS

Answer 3

The graph of the quadratic is a parabola.
The directrix is horizontal, so the parabola is vertical.
The focus lies below the directrix, so the parabola opens downwards.
General equation of a down-opening parabola:

y = a(x - h)² + k
with
a < 0
vertex (h, k)
focal length p = | 1/(4a) |
focus (h, k-p)
directrix y = k+p

Plug your data into the equations and solve for a.