Plug the points that are given in.

-2=9a+3b+c

0=4a+2b+c

We need a third equation to solve. We are given the vertex; so the symmetrical line of this parabola is x=3. Reflect the other given point, (2,0), over this line to get your third point (4,0).

0=16a+4b+c. 3rd equation minus second equation is 12a+2b=0, second equation minus the first is -5a-b=2. -10a-2b=4. 2a=4, a=2, b=-12, c=16. (2,-12,16)