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

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

Answer 1

The zeros are the points where the parabola crosses the x axis, and represents the the breakeven (no profit, no loss) points.

\[[-2,500\pm \sqrt{-2500^{2}-(4)(-250)(-4000)}]/(2)(-250)\]\[[-2500\pm \sqrt{2,250}]/-500\]\[[-2,500\pm1,500]/-500\]\[-1000/-500 = 2\]\[-4000/-500 = 8\]The zeros are x=2 x=8

Part B

\[-250n ^{2}+2500n-4000=0\]\[[-250][n ^{2}-10n+16]=0\]\[[-250][n ^{2}-10n=25-25+16]=0\]\[[-250][n ^{2}-10n+25-9]=0\]\[[-250][(n-5)^{2}-9]=0\]Maximum profit occurs when n=5
Substitute into the original equation.\[P(5)=-250(5^{2})+2500(5)-4000\]\[P(5)=$2,250\]

Part C
Axis of symmetry at x=5

Answer 2

Thank you.

Answer 3

yw