Question

write the equations of the parabola, the directrix, and the axis of symmetry.

vertex: (-4,2)
focus: (-4,6)

if someone could explain how to do this problem then that would be great! thanks in advance!

Formats to help you find the equation for a parabola:
(x - h)^2 = 4p(y - k)
Vertex = (h, k)
Focus = (h, k + p)
Directrix: y = k - p

You are given the vertex (-4,2) and the focus (-4,6).

Since we know k, which is 2, we can figure out p. Format = (h, k + p) for focus. Therefore, p = 4.

I'll set this up and let you take it from there:
[x - (-4)]^2 = 4(4)(y - 2)

The axis of symmetry is: x = -4 (vertex x-value).

I hope this will help.

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it did. thanks so much!

Thanks Bob! Just happy to help. :)

Answer 1

x^2=-24y