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)
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