Question

What equation represents a parabola opening downward with a vertex at the origin and the focus at (0,-2)

Answer 1

opens downwards, means is opening vertically or over the y-axis
so the "focus form" for that will be => \(\bf (x-h)^2=4p(y-k)\)

vertex is at (h, k) points
p = distance from the vertex to the focus

Answer 2

"p" is negative if the parabola opens downwards, positive if upwards