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 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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the maximum profit is 2,250 and the steps of finding it are right here ~>
>first you need to factor out -250 from the equation, (n)=−250(n^2 −10n)−4000
> then you take half of -10 and its -5, and we need to square -5 which gets us positive 25, P(n)=−250(n^2 −10n+25)−4000
> but we cannot do this cause now the equation isn't balanced, and we need to balance it...which means we need to take the 25 out, so we subtract the 25 out of the brackets, P(n)=−250(n^2 −10n+25 - 25)−4000
>now we need to multiply the -25 by -250 it make it a different number, P(n)=−250(n^2 −10n+25)+6250−4000
. > now we add the last terms together to get the following P(n)=−250(n^2 −10n+25)+2,250
> now we factor the following (n^2 −10n+25) by grouping, so like this n^2 - 5n -5n +25 ~> n(n - 5) -5(n - 5) ~> (n - 5)^2
> so now we get P(n)=−250(n−5)^2 +2,250
Part C: the axis of symmetry of the function P(n) is x = 5
Thank you so much! can you help me with one more question?
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The area of a rectangular piece of land is 240 square meters.
If the length of the land was 5 meters less and the width was 3 meters more, the shape of the land would be a square.
Part A: Write an equation to find the width (x) of the land. Show the steps of your work.
Part B: What is the width of the land in meters? Show the steps of your work.
Part A: (x + 3)(x - 5) = 240
>The rectangular area is : xy = 240, and the square area is, (x + 3)(y - 5) = 240
>(x + 3)(x - 5) = 260
> x^2 - 2x - 15 = 260
> x^2 - 3x - 240 = 0
> (x +15)(x - 17) = 0
> x - 17 = 0
> x + 15 = 0
Part B: and to find the width of the land you need to solve x - 15 = 0, which is 15 or x=15.
Thank you so so so much!
your so so so welcome :)
@only_hanaaa I have a question with the part b, wouldn't it be x + 15 = 0 making x = -15?