I made a big mistake, my apologies. The normal form should be
. There are three variables to solve for, a b and c. So you need three pairs of (x,y) points to be able to solve for a b and c. G(x) gives you three points but for F(x) you have to use the fact that the parabola is symmetrical to get a third point.
Since you have the point (4,2) you can deduce that there is also the point (3,2) on the graph. Now you plug in your three (x,y) pairs into the equation I wrote above and solve for your a, b and c.