Write a quadratic function in vertex form whose graph that has the given characteristics:

a.) vertex at (0,0), passing through the point (6, -9)

The answer is: y= -1/4x^2 But I am not sure how the variable (x^2) fits in there...

I've gotten this far but I believe I am going in the wrong direction...

y=a(x-p)^2+q

-9=a(6-0)^2+0

-9=36a

-1/4=a

b.) vertex (0, -6), passing through the point (3, 21)

If you could help me with these, I would greatly appreciate it. Thank you so much!!