Question

How do you find the vertex, focus, and directrix of a parabola `(y-9)^2 = -8(x+5)`?

Answer 1

A Guide
If you got a parabola in the form `(y - y_v)^2 =4a(x-x_v)`

Then `(x_v, y_v)` is your vertex,

Focus is `(x_v +a , y_v)`

and directrix is the line `x=x_v-a`

Solution to problem

`(y-9)^2=-8(x+5)`

`-= (y-9)^2= 4(-2)(x-(-5))`

Vertex is `(-5, 9)`

It can be seen by comparison with the general form that `a= -2`

Implying that,

Focus is `(-5+(-2), 9)` or `(-7,9)`

Directrix is `x = -5-(-2)` or `x=-3`

Verify on the graph
graph{sqrt(-8x-40)+9 [-6.75, 13.25, -4.24, 5.76]}