# algebra 2

revenue from ticket sales: 4x(x+6)
cost of band: 5x(x-4)
profit: 160 (given in thousands, use 160)
1.the equation to determine profit id revenue-cost=profit. write the equation that explains the profit made last year. be certaiin to combine like terms.
if you graphed this equation, would the graph open up or down? how could you telll without grapahing?
2. if you graphed this would it be open up or down & how could you tell without graphing?
3. given the shape of the graph what happened to ticket sales as time passed?
4. given the equation you arrived at in question1 what 2 days were the break evenpoints for ticket sales.
5.at what day did the peak oof profit from ticket sales occur?
6. at that day, what was the profit from ticket sales?
7. what was the vertex of the graphrd lines?
8. logical conclusion: as you look at the graph, what day do you believe the committee shouldhave stopped attempting to sell tickets? Explain.

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1. 4x(x+6) - 5x(x-4) = p

4 x^2 + 24 x - 5 x^2 + 20 x = p

-x^2 + 44 x = p
or
x^2 -44 x = -p
as x gets big, the x^2 term dominates and profit is negative. Therefore the parabola opens down (sheds water)
3. sales increase with x. but band costs increase faster.
4. the profit is zero when x = 0 and when x = 44
5. find vertex by completing square
x^2 - 44 x + 22^2 = -p + 484
(x-22)^2 = - (p-484)
so at x = 22
6, then the profit was 484
7. That is the vertex (22,484)
8. at 22 days the profit is maximum.

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