## anonymous one year ago The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each: P(n) = -250n^2 + 2,500n - 5,250 Part A: What are the zeroes of the above function, and what do they represent? Show your work.

1. anonymous

@SolomonZelman

2. SolomonZelman

What does n represent?

3. anonymous

dollars

4. SolomonZelman

precisely, n, is a price per ticket.

5. SolomonZelman

What does P(n) represent?

6. anonymous

profit

7. SolomonZelman

Yes, when P(n) is 0, that means that the profit is zero (i.e. made nothing), right?

8. anonymous

yes

9. SolomonZelman

The x-intercepts of this function are the values of n (or the value of the price per ticket) with which the P(n) (or the profit) is 0. (There are going to be 2 x-intercepts)

10. anonymous

okay

11. SolomonZelman

So, if you find the x-intercepts, you are going to find the 2 possible values of a price per ticket with which the promoter will NOT profit (but will not lose).

12. SolomonZelman

So, do you see what these x-intercepts would mean?

13. anonymous

yes

14. SolomonZelman

Ok, now you have to solve for these x-intercepts.

15. anonymous

the x intercepts are 3 and 7?

16. SolomonZelman

yes, very good!

17. SolomonZelman

Perfect!

18. SolomonZelman

So, when the ticket costs 3$or 7$ , then the promoter doesn't gain or lose.

19. anonymous

now what?

20. SolomonZelman

when the *average* ticket I should say

21. SolomonZelman

Well, all you had to do is to find these zero (these x-intercepts), and to then say what these x-intercepts represent in your situtation.

22. SolomonZelman

you found x=3, and x=7 ((( and that is correct ))) now you have to say what do these intercepts mean/do/represent?

23. SolomonZelman

just say what we have agreed on in the beginning.

24. anonymous

can you help me with part B?

25. SolomonZelman

what is part B?

26. SolomonZelman

I can try my best with it:)

27. anonymous

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

28. SolomonZelman

Oh, good

29. SolomonZelman

 SIDE - NOTE: Most people would say that this question requires calculus, but in a case of a parabola (a quadratic does not). (this what most people say is a mistake).  ALL YOU GOT TO DO: You have to write your P(n) in a vertex form, and the vertex is going to be the maximum.

30. anonymous

so (5,1000)?

31. SolomonZelman

Let me see.... i wil be typing, and if it is right I will post the work, and if it is not, then I will ask you to redo it and follow along with me.

32. SolomonZelman

hope that is fair.

33. anonymous

yes

34. SolomonZelman

$$\large\color{black}{ \displaystyle P(n) = -250{\rm n}^2 + 2,500{\rm n} - 5,250 }$$ $$\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}) - 5,250 }$$ $$\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25-25) - 5,250 }$$ $$\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25)+(-250)(-25) - 5,250 }$$ $$\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25)+1000 }$$ $$\large\color{black}{ \displaystyle P(n) = -250({\rm n}-5)^2+1000 }$$

35. SolomonZelman

yes, that is correct

36. SolomonZelman

And quite quick

37. anonymous

1 graphed it

38. SolomonZelman

oh, you graphed it... good, but it is very good (I would insist that even required) to know that without graphing.... in any case though, lets do a little review of what you have actually found just now,

39. anonymous

the axis of symmetry would be 5 right? (Thats part C)

40. anonymous

okay

41. SolomonZelman

yes part C is correct

42. SolomonZelman

now the review of what does the vertex of (5,1000) actually mean in this case.

43. anonymous

thats the maximum about of profit the promoter can make?

44. SolomonZelman

that is you are refering to the point to a 5 or a 1000 ?

45. anonymous

1000 makes more sense 1 think

46. SolomonZelman

yes

47. SolomonZelman

and what does 5 mean, can you tell me?

48. anonymous

the amount the tickets cost?

49. SolomonZelman

yes

50. SolomonZelman

So when the average ticket costs 5\$, you get a maximum profit of 1000

51. anonymous

makes sense

52. SolomonZelman

A quite small, if not miserable profit in a real life situation... but won't be talking about a real life situation because such situations are never modeled with quadratics in real life....

53. SolomonZelman

yeah, so you got any questions regarding any of the PARTS ?

54. anonymous

nope thats it

55. anonymous

as usual you're the most helpful person on the whole site. Thanks!

56. SolomonZelman

$$\large{\bbox[5pt, cyan ,border:2px solid black ]{ \rm Thanks! }}$$

57. SolomonZelman

I wouldn't say I am most helpful, but won't deny some use.; you are always welcome!