Say the last two digits of your ID are 3 and 9. (I just picked them randomly.) So 3 + 9 = 12.

So

a) We need a quadratic function passing through the points (12, 0), (13, 0), and (0, 14).

The general quadratic function (assuming we want the parabola to open up or down) is

So we know that

and

and

Thus

and

Solve for a and b.

b) The vertex form of a quadratic would be more handy here:

This is a parabola with a vertex at (h, k).

So we need a vertex at (12, -12) and y-intercept at (0, 3). From the vertex:

Putting in the point (0, 3):

which you can solve for a.

-Dan