Find the vertex, focus, directrix, and focal width of the parabola: - 1/40x^2=y

For

(x-h) ^2=4p (y-k)

vertex is (h, k)

distance from vertex to directix=p=distance from vertex to focus

|4p|=focal width

remember, focus is on the side of the parabola where it opens and directix is at the back

when p is negative, it opens down

when p is positive, it opens up

look at equation

-1/40 (x-0) ^2 = (y-0)

times - 40 to both sides

(x-0) ^2=-40 (y-0)

(x-0) ^2=4 (-10) (y-0)

vertex = (0,0)

p=-10, it's negative so it opens down

focus is 10 units below vertex (y direction)

focus = (0,-10)

diretix is 10 above

directix is y=10

focal width=|4p|=|4 (-10) |=|-40|=40

vertex = (0,0)

focus = (0,-10)

directix is y=10

focal width=40 units