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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 :

the  x coordiante of the vertex  = -b/2a  = -48 / -2 = 24
and y coordinate =  -(24)^2 + 48(24) - 432 =  144

so the vertex is at (24,144)

This represents the maximum profit that can be made  - $144 if you sell 24 games.

B.  solve for x:-

-x^2 + 48x - 432 = 0

-(x  - 36)(x - 12) = 0

so the x intercepts are at 12,0) and (36,0)
selling 12  or 36 games will give zero profit  ( that is the break even points).

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