FAN AND MEDAL!! 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)

Question

FAN AND MEDAL!! 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)

heyitszia1 · Answer

I know that the vertex is (24,144), but I need help finding the x-intercepts.

heyitszia1 · Answer

#math&ing001

heyitszia1 · Answer

@Whitemonsterbunny17

heyitszia1 · Answer

@Aveline

heyitszia1 · Answer

I need help with part B

aveline · Answer

−x² + 48x − 432
To find the vertex, you use -b/2a
a=-1 b=48 c=-432
So, the x value of the vertex is equal to:
-48/-2
(24,144)

aveline · Answer

Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Let's simplify the equation:
$$x ^{2}-48x+432=0$$
$$(x-12)(x-36)=0$$

aveline · Answer

This means that the x-intercepts are at 12 and 36

aveline · Answer

I divided by -1 to make -x^2 positive

heyitszia1 · Answer

Did you factor the equation to get (x - 12) and (x - 36)?

aveline · Answer

yes

heyitszia1 · Answer

Thanks :)