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)
i have the vertex and the x-intercepts but i need to know what they mean in the context of the problem.

Part A : The vertex is (12,60) . this tells us that the maximum amount of profit  i.e. 60 is obtained by selling 12 cups of coffee.

Part B: x-intercept are 4 and 20

x intercept means the number of cups of coffee sold when the amount of profit is 0.

Step-by-step explanation:

Given :

The function 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.

Solution:

Standard equation:

where (h,k) is the vertex

Convert the given equation in standard form.

Thus the vertex is (12,60)

Part A : The vertex is (12,60) . this tells us that the maximum amount of profit  i.e. 60 is obtained by selling 12 cups of coffee.

Part B: x-intercept

To Find x intercept substitute y =0

So, x-intercept are 4 and 20

x intercept means the number of cups of coffee sold when the amount of profit is 0.

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

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