Question

PLEASE HELP 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)

Answer 1

`f(x) = -x^2 + 48x - 432`

Part A

Find the zeros:


`x^2 - 48x + 432 = 0`

Factor


`(x - 36 ) (x - 12 )=0`

Two solutions: x = 36 and x = 12

The vertex is in
`x = ( (36 +12 ))/(2 = 24)`


`f(24) = -(24)^2 + 48(24) - 432 = 144`

The vertex is (24, 144).

The coefficient of
`x^(2)` 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!