The graph of a quadratic function is (6,0) and (p,0). the maximum point has coordinates (0.5,30.25). what is the value of p?

The roots of a parabola are symmetrical with respect to the vertex (in this case the maximum).

So, if the vertex lies at x=0.5, and one solution lies at x=6 (i.e. 5.5 units to the right of the vertex), the other solution must lie 5.5 units to the left of the vertex, i.e. at x=0.5-5.5 = -5.

So, the two solutions are (-5, 0) and (6, 0)