You can
put this solution on YOUR website!You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).
Tickets: E(x) = -0.2x^2+12x+11
a. Does the graph of this equation open up or down?
Ans: down because the coefficient of the highest power term is negative.
How did you determine this?
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b. Describe what happens to the tickets sales as time passes?
Number of ticket sales goes down to zero.
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c. Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)
Solve E(x) = 0 for "x>0".
x = [-12 +- sqrt(144-4*-0.2*11)]/(-0.4)
x = [-12 +- sqrt(152.8)]/(-0.4)
Positive solution:
x = [-12-12.36]/-0.4
x = 60.9 days
On the 61st day, the ticket sales go to zero.
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d. Will tickets peak or be at a low during the middle of the sale? How do you know?
Ans: Peak; the parabola has a maximum point.
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e. After how many days will the peak or low occur?
30 th day
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f. How many tickets will be sold on the day when the peak or low occurs?
E(30) = 191
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g. What is the point of the vertex? (30,191)
(How does this number relate to your answers in parts e and f?
h. How many solutions are there to the equation ?
2 because it is a quadratic.
How do you know?
i. What do the solutions represent?
The two days when ticket sales are zero.
Is there a solution that does not make sense?
Yes: x = -0.90
If so, in what ways does the solution not make sense?
-0.90 is one day before sales began.
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Cheers,
Stan H.
