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? (5 points)
Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

Answer 1

vertex tells us the how many games to sell to get the maximum profit in this case :)

to find the vertex of the equation in the form of ax^2 + bx + c, the x-coordinate of the vertex is -b/2a
you then plug that in to the equation to get the y-value of the vertex

can you find the vertex? (:

Answer 2

i'm not sure how

Answer 3

is it 24,144

Answer 4

correct! (24, 144) is correct (:

Answer 5

to find the x-intercepts, you plug in y = 0 and solve the quadratic equation

Answer 6

so the answer for part a would be the vertex of this function is (24,144) which means The turning point of a parabola and for part b the x-intercepts for this function are (12,0) and (36,0) which means The point where a line crosses the x-axis. The value of x when y = 0 ?

Answer 7

it wants to know what the vertex means in the context of the situation

it means that when you produce 24 games, you make the maximum profit of 144

you got the x-intercepts correct, but try to find what those values mean in the context

hint: y = 0 means you make no money :P

Answer 8

what do i write for part b

Answer 9

"What do these values mean in the context of the problem?"

So when we produce 12 games and 36 games, how much profit do you make?

Answer 10

i'm not sure what the context is

Answer 11

basically, what happens if we produce 12 games or 36 games? What is the profit? What is the y-value?