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? (5 points)

part b: determine the x-intercepts. what do these values mean in the context of the problem? (5 points)

The function is graphed as shown below

Part A:

We use the formula to find the vertex of the function. A quadratic function of the form of and equating this form to the given function , we have
and .

Substituting and into the vertex formula, we have
, as shown in the graph

This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising





and , as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos