Me
the function f(x) = −x2 + 48x − 432 models the profit, in dollars, a game developer makes for selling a new game, where x is the number of games 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)

Part A

Find the zeros:



Factor



Two solutions: x = 36 and x = 12

The vertex is in



The vertex is (24, 144).

The coefficient of  is negative, the parabola opens downward, that mean that the vertex is a maximum value.

In the context of the problem that means that the maximum profit is 144 and is obtained when the number of games sold is 24.

Part B.

The x-intercepts are the values of x when y=0. 

 x = 24 and x = 36.

Those values are the number of games for which the profit is zero.

Hope I helped!