anonymous
  • anonymous
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)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[P(n) = -250n^2 + 2,500n - 4,000 \] you want the zeros?
anonymous
  • anonymous
I already finished part A I know the 0's are 2 and 8
anonymous
  • anonymous
no that is wrong

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anonymous
  • anonymous
\(n\) is the price i guess if he prices the tickets at $2 or at $8 he makes no money
anonymous
  • anonymous
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.
anonymous
  • anonymous
is that correct?
anonymous
  • anonymous
yes looks good to me
anonymous
  • anonymous
Okay (:
anonymous
  • anonymous
Now how do I "complete the square"
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
plus the first coordinate of the vertex is always \[-\frac{b}{2a}\] which in your case is \[-\frac{2500}{2\times (-250)}=5\]
anonymous
  • anonymous
Yeah, but it specifically asks to complete the square (which I hate because it's so confusing)
anonymous
  • anonymous
but we can still complete the square if you are dying to do it
anonymous
  • anonymous
factor out the \(-250\) from the first two terms
anonymous
  • anonymous
\[ -250n^2 + 2,500n - 4,000 \] \[-250(n^2-10n)-4,000\]
anonymous
  • anonymous
P(n)=-250(n^2-10n)-4000?
anonymous
  • anonymous
Okay i got that aha
anonymous
  • anonymous
right that is step one
anonymous
  • anonymous
then half of \(-10\) is \(-5\) complete the square via \[-250(n-5)^2-4000+25\times 250\]
anonymous
  • anonymous
Yeah... I got lost there ):
anonymous
  • anonymous
yeah i can see why
anonymous
  • anonymous
when you replace \(n^2-10n\) by \(n-5)^2\) you have changed it
anonymous
  • anonymous
\[(n-5)^2=n^2-10n+25\] so you have added \(25\) when you make the change
anonymous
  • anonymous
Ohh, okay I see that now, but like if it's so many numbers and such, my brain likes to just stop reading it
anonymous
  • anonymous
why 25 though?
anonymous
  • anonymous
because when you square \(n-5\) you get \((n-5)^2=n^2-10n+25\)
anonymous
  • anonymous
Ohhh
anonymous
  • anonymous
Okay (:
anonymous
  • anonymous
now don't forget the \(-250\) outside the parentheses
anonymous
  • anonymous
so actually you have subtracted \(25\times 250\) so you have to add it back
anonymous
  • anonymous
hence \[-250(n-5)^2-4000+25\times 250\]
anonymous
  • anonymous
but why the times symbol?
anonymous
  • anonymous
what else would you like me to write? look at this line \[-250(n-5)^2\]
anonymous
  • anonymous
if you multiply that out you get \[-250(n^2-10n+25)\] as a first step
anonymous
  • anonymous
I meant the times symbol for 25 x 250
anonymous
  • anonymous
and when you multiply that out, you get \[-250n^2+2500n-6250\]
anonymous
  • anonymous
you subtracted \(6250\) from the original expression, so you have to add it back
anonymous
  • anonymous
there is really a much much easier way to do it
anonymous
  • anonymous
Yeah, but my algebra teachers just love making us suffer haha
anonymous
  • anonymous
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 \(P(5)\)
anonymous
  • anonymous
you can pretend to to it the other way, but then just find \(P(5)\) and write that out at the end
anonymous
  • anonymous
so after P(n)=-250(n-5)^2-4000+25*250 ,what do I do, or is that the final step?
anonymous
  • anonymous
algebra teachers lead sad lives, most are either frustrated mathematicians or are teaching at the outer edge of their knowledge
anonymous
  • anonymous
compute the number at the end
anonymous
  • anonymous
-250(n-5)^2-4000+6250
anonymous
  • anonymous
\[-400+25\times 250=2250\]
anonymous
  • anonymous
-250(n-5)^2+2250
anonymous
  • anonymous
yes
anonymous
  • anonymous
And now? do I make it (n-5)(n-5)?
anonymous
  • anonymous

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