The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit.

part a: determine the vertex. what does this calculation mean in the context of the problem?

part b: determine the x-intercepts. what do these values mean in the context of the problem?

f(x) = -x^2 + 20x - 75 = (x-5)*(-x + 15)
The two x-intercepts are x = 5 and x = 15, which are the two values of x where f(x) = 0. The vertex is located halfway between these two points, so where x = 10. When x = 10, f(x) = 25, so the vertex of this graph is (10, 25).

Part A: The vertex is (10, 25). The vertex represents the point where the profit is a maximum. When 10 photos are printed, the profit is $25.

Part B: The two x-intercepts are x = 5 and x = 15. This shows where the profit is $0. When 5 photos or 15 photos are printed, the profit is $0.