The quadratic function f(x) = p + qx – x^2 has a maximum value of 5 when x = 3. Find the value of p and the value of q.

Express the quadratic equation using the formula that uses the vertex (x and y of the minimum/ maximum value). The formula is f(x)=a(x-h)^2 + k, where h=-b/2a and k=f(h). Now we have that a=-1 from the problem. We have that (3,5) is the vertex. Therefore, y= - (x-3)^2 + 5 (=) -x^2 + 6x - 4 So, q= 6, p= -4