Me plz asap. 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)

Remark

Yesterday and today make it very dangerous to answer any math question. I'm going to see if I can answer this without the editor throwing up. The method is worked out now that I can see that the bug might have been fixed.

The final answer is y = -(x - 24)^2 + 144

The first thing to do is to complete the square.

y = -(x^2 - 48x ) - 432

y = -(x^2 - 48x + (48/2)^2 ) - 432 + 24^2

y = -(x - 24)^2 + 576 - 432

y = -(x - 24)^2 + 144

The vertex is (24,144)

Explanation

It means that when 24 games are sold, the profit is a maximum 144 dollars.  You can convince yourself of that by trying a couple of numbers.  Try x = 28. If you sell 28 games the following will happen.

y = -(28 - 24)^2 + 144

y = - 4^2 + 144

y = -16 + 144

y = 128 which is less that 144. 

You could also try 20 which will give you the same  answer 128

Problem B

What are the x intercepts?

y = -x^2 + 48x - 432

You do not need the quadratic equation for this. It factors. 

y = -(x - 12)(x - 36)

when y = 0 then either 

x - 12 = 0

x = 12

When x = 12 the profit is 0. He starts to make money at x = 13

or

x - 36 = 0

x = 36

also he his making nothing when x = 36 which seems odd because you would think that the more you sell the more you make, but the quadratic makes this a limiting consideration. 

So x<12 loses money

x>36 looses money

12<x<36 is where he makes some money.

answer: b.48 for

step-by-step explanation: