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anonymous

  • one year ago

Fan and Medal! 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 - 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)

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  1. anonymous
    • one year ago
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    \[P(n) = -250n^2 + 2,500n - 4,000 \] you want the zeros?

  2. anonymous
    • one year ago
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    I already finished part A I know the 0's are 2 and 8

  3. anonymous
    • one year ago
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    no that is wrong

  4. anonymous
    • one year ago
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    \(n\) is the price i guess if he prices the tickets at $2 or at $8 he makes no money

  5. anonymous
    • one year ago
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    The zeroes of the function would be 2 and 8. The zeroes of the function above represents the specific prices, 2 and 8, which will result in a zero profit.

  6. anonymous
    • one year ago
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    is that correct?

  7. anonymous
    • one year ago
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    yes looks good to me

  8. anonymous
    • one year ago
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    Okay (:

  9. anonymous
    • one year ago
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    Now how do I "complete the square"

  10. anonymous
    • one year ago
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    there is a much easier way to do it (find the max) than completing the square, but we can do it that way too if you have to

  11. anonymous
    • one year ago
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    first of all it is pretty obvious that if it is zero at 2 and at 8 then it is the biggest half way between at 5

  12. anonymous
    • one year ago
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    plus the first coordinate of the vertex is always \[-\frac{b}{2a}\] which in your case is \[-\frac{2500}{2\times (-250)}=5\]

  13. anonymous
    • one year ago
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    Yeah, but it specifically asks to complete the square (which I hate because it's so confusing)

  14. anonymous
    • one year ago
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    but we can still complete the square if you are dying to do it

  15. anonymous
    • one year ago
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    factor out the \(-250\) from the first two terms

  16. anonymous
    • one year ago
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    \[ -250n^2 + 2,500n - 4,000 \] \[-250(n^2-10n)-4,000\]

  17. anonymous
    • one year ago
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    P(n)=-250(n^2-10n)-4000?

  18. anonymous
    • one year ago
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    Okay i got that aha

  19. anonymous
    • one year ago
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    right that is step one

  20. anonymous
    • one year ago
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    then half of \(-10\) is \(-5\) complete the square via \[-250(n-5)^2-4000+25\times 250\]

  21. anonymous
    • one year ago
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    Yeah... I got lost there ):

  22. anonymous
    • one year ago
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    yeah i can see why

  23. anonymous
    • one year ago
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    when you replace \(n^2-10n\) by \(n-5)^2\) you have changed it

  24. anonymous
    • one year ago
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    \[(n-5)^2=n^2-10n+25\] so you have added \(25\) when you make the change

  25. anonymous
    • one year ago
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    Ohh, okay I see that now, but like if it's so many numbers and such, my brain likes to just stop reading it

  26. anonymous
    • one year ago
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    why 25 though?

  27. anonymous
    • one year ago
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    because when you square \(n-5\) you get \((n-5)^2=n^2-10n+25\)

  28. anonymous
    • one year ago
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    Ohhh

  29. anonymous
    • one year ago
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    Okay (:

  30. anonymous
    • one year ago
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    now don't forget the \(-250\) outside the parentheses

  31. anonymous
    • one year ago
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    so actually you have subtracted \(25\times 250\) so you have to add it back

  32. anonymous
    • one year ago
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    hence \[-250(n-5)^2-4000+25\times 250\]

  33. anonymous
    • one year ago
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    but why the times symbol?

  34. anonymous
    • one year ago
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    what else would you like me to write? look at this line \[-250(n-5)^2\]

  35. anonymous
    • one year ago
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    if you multiply that out you get \[-250(n^2-10n+25)\] as a first step

  36. anonymous
    • one year ago
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    I meant the times symbol for 25 x 250

  37. anonymous
    • one year ago
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    and when you multiply that out, you get \[-250n^2+2500n-6250\]

  38. anonymous
    • one year ago
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    you subtracted \(6250\) from the original expression, so you have to add it back

  39. anonymous
    • one year ago
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    there is really a much much easier way to do it

  40. anonymous
    • one year ago
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    Yeah, but my algebra teachers just love making us suffer haha

  41. anonymous
    • one year ago
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    since you know that the first coordinate of the vertex is \(5\) if you want the second coordinate, all you have to do is find \(P(5)\)

  42. anonymous
    • one year ago
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    you can pretend to to it the other way, but then just find \(P(5)\) and write that out at the end

  43. anonymous
    • one year ago
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    so after P(n)=-250(n-5)^2-4000+25*250 ,what do I do, or is that the final step?

  44. anonymous
    • one year ago
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    algebra teachers lead sad lives, most are either frustrated mathematicians or are teaching at the outer edge of their knowledge

  45. anonymous
    • one year ago
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    compute the number at the end

  46. anonymous
    • one year ago
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    -250(n-5)^2-4000+6250

  47. anonymous
    • one year ago
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    \[-400+25\times 250=2250\]

  48. anonymous
    • one year ago
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    -250(n-5)^2+2250

  49. anonymous
    • one year ago
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    yes

  50. anonymous
    • one year ago
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    And now? do I make it (n-5)(n-5)?

  51. anonymous
    • one year ago
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    @perl

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