The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each:

P(n) = -250n2 + 2,500n - 4,000

Part A: What are the zeroes of the above function, and what do they represent? Show your work. (4 points)

Part B: Find the maximum profit by completing the square of the function P(n). Show the steps of your work. (4 points)

Part C: What is the axis of symmetry of the function P(n)? (2 points)

Question

The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each:

P(n) = -250n2 + 2,500n - 4,000

Part A: What are the zeroes of the above function, and what do they represent? Show your work. (4 points)

Part B: Find the maximum profit by completing the square of the function P(n). Show the steps of your work. (4 points)

Part C: What is the axis of symmetry of the function P(n)? (2 points)

hellokitty17 · Answer

@HootHoot

hoothoot · Answer

ok im trying this one throwing me off a bit

hellokitty17 · Answer

ok! thanks

hoothoot · Answer

one year ago

$$\Large\rm P(n)=-250n^2 + 2500n - 4000$$So the find `zeros`, we set the P(n) equal to zero.$$\Large\rm 0=-250n^2 + 2500n - 4000$$This will be easier to work with if we have no fancy coefficient on the squared term.
So let's factor a -250 out of each term:$$\Large\rm 0=-250(n^2-10n+16)$$Then divide the -250 away,$$\Large\rm 0=n^2-10n+16$$It looks like this will factor nicely!
Confused by any of those steps?

hoothoot · Answer

few dont wanna write that back down again

hellokitty17 · Answer

Witch part is witch

hellokitty17 · Answer

@HootHoot

oregonduck · Answer

which one is part a b and c?

hoothoot · Answer

the mid is and the lower part is c i go from top to bottom

hoothoot · Answer

orry it is a lil confusing

hoothoot · Answer

but that was the best way to explain it the other ways made it harder to understand

hellokitty17 · Answer

could you writ is again please with it saying part a b and c

oregonduck · Answer

-250n^2 + 2500n - 4000 = 0 
n^2 - 10n + 16 = 0 
(n - 8)(n - 2) = 0 

The zeroes are (0,2) and (0,8). The values between these two points are places where the profit is positive. At these two points, the promoter breaks even. 

*** 

n^2 - 10n + 16 = 0 
-10/2 = -5 
(-5)^2 = 25 
n^2 - 10n + 25 = 9 
(n - 5)^2 = 9 

The maximum is when n - 5 = 0, or n = 5. P(5) = 9 * 250 = 2250, or (5,2250). 

*** 

The access of symmetry is at n = 5.

hoothoot · Answer

-250n^2 + 2500n - 4000 = 0 n^2 - 10n + 16 = 0 (n - 8)(n - 2) = 0 




The zeroes are (0,2) and (0,8). The values between these two points are places where the profit is positive. At these two points, the promoter breaks even. 

n^2 - 10n + 16 = 0 -10/2 = -5 (-5)^2 = 25 n^2 - 10n + 25 = 9 (n - 5)^2 = 9 The maximum is when n - 5 = 0, or n = 5. P(5) = 9 * 250 = 2250, or (5,2250). The access of symmetry is at n = 5. ok i tried my best hope this works

hoothoot · Answer

my finger gett sore from typing