Question

What is the equation of the following graph?

Answer 1

Its a negative parabola, where a < 0

Answer 2

okay...

Answer 3

The parent function for parabolas is f(x) = x^2

You can use the parent function to apply the needed transformations to get the equation that's needed.

Answer 4

f(x) = -(9/4)x^2

The vertex form is usually defined as f(x) = a((x-h)^2)+k
Where the sign of "a" (positive or negative) defines whether it opens up or down.
"a" itself is it's aperture. The only points I could find from your graph (besides the origin) were (9,-4) and (-9,-4). The rule of correspondence would be -(9/4) which is basically taking the slope to the origin (difference in y / difference in x).

"h" and "k" would be 0 for (h,k) is the vertex and the vertex is the origin (0,0).

The image is too vague, but that's as close as you can get.