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
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.