Question

The function f(x) = –x2 + 24x – 80 models the hourly profit, in dollars, a shop makes for selling coffee, where x is the number of cups of coffee sold, 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)

Answer 1

The first step is to draw the graph. Once we do this, we can easily see that the vertex is at (12,64), which means that the hourly profit of coffee sold is highest at 12 cups of coffee. The x-intercepts are at x = 4 and x = 20, which means that between 0 and 4 (inclusive) cups of coffee sold, and after 20 cups sold, there is no profit.