Question

Find the equation of a parabola whose vertex is at the origin and whose focus is (0, -2)

Answer 1

Use the formula for vertex form a(x+h)^2+k
Plug in the given vertex into the formula
So (x+0)^2-2
Since there is not a value for h the equation is just x^2-2
I hope this helps!

Answer 2

x^2 = -8y

Explanation:

The coordinates of the focus are of the form (0, a). So, the parabola has a vertical axis and a = -2.

Use the focus-directrix equation form for a parabola with a vertical axis and its vertex at the origin to get:

x2 = 4ay

x2 = 4(-2)y