Question

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?

what i've got so far is y=-1(x^2-48+576-576+432)
y=-1[(x-24)^2-144). I believe I am right and am confused about the next part o the problem. I will award medals.

Answer 1

Part B: Determine the x-intercepts. What do these values mean in the context of the problem?
I have gotten that the answer is (12,0) and (36,0) but i do no9t know what the represent in the context of the problem.

Answer 2

f(x) = −x2 + 48x − 432
= -1(x - 24)^2 + 144

so the vertex would be (24, 144) right ?

Answer 3

Yes, that is what I was thinking but wasn't sure if it was correct

Answer 4

As you can see, a parabola has only one vertex point.

Answer 5

Notice that vertex is the top of the hill. The maximum point.

Answer 6

In our problem, what do x and f(x) represent ?

Answer 7

x is the number of games sold and f(x) is the amount of profit

Answer 8

f(x)=y

Answer 9

Since the maximum value occurs at the vertex, what does the point (24, 144) represent here ?

Answer 10

24 is the max amount of games sold. 144 is the amount of profit.

Answer 11

Can we say that the maximum value of the profit is 144, and it occurs when 24 games are sold ?

Answer 12

yes i agree lol

Answer 13

24 is the number of games to be sold to achieve the maximum profit
144 is the maximum profit

Answer 14

Good :)

Answer 15

Im still little confused about part b though :/

Answer 16

@ganeshie8 ^^^