Question 473531: 1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. 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).
a. Does the graph of this equation open up or down? How did you determine this?
b. Describe what happens to the tickets sales as time passes.
Ticket sales increase until a peak is reached then the sales decrease
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.
d. Will tickets peak or be at a low during the middle of the sale? How do you know?
e. After how many days will the peak or low occur?
f. How many tickets will be sold on the day when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?
h. How many solutions are there to the equation ? How do you know?
i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
This is what I have so far
0.2x^2 + 12 x + 11
0.2(x^2 -24x + 144 - 144) + 12
0.2(x-24 + 144) + 12+72
0.2*x-12)^2 = 86
The peak would be 12 days after the tickets go on sale and the ticket sale would end in 86 days
Am I on the right track?
Found 2 solutions by stanbon, ccs2011:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day -0.2x^2 + 12 x + 11 where x is the day tickets go on sale
a. Does the graph of this equation open up or down? How did you determine this?
Ans: up then down because the coefficient of x^2 is negative
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b. Describe what happens to the tickets sales as time passes.
Ticket sales increase until a peak is reached then the sales decrease
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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 -0.2x^2 + 12 x + 11 = 0
Use the quadratic formula to get x = 60.9
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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
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e. After how many days will the peak or low occur?
Ans: 30
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f. How many tickets will be sold on the day when the peak or low occurs?
Ans: f(30) = 191
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g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?
Ans: (30,191)
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h. How many solutions are there to the equation ?:::2
::How do you know? Quadratic equation with positive discriminant.
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i. What do the solutions represent? Is there a solution that does not make sense?
Yes: x = -1
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If so, in what ways does the solution not make sense?
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This is what I have so far
-0.2x^2 + 12 x + 11
-0.2(x^2 -24x + 144 - 144) + 12
-0.2(x-24 + 144) + 12+72
-0.2*x-12)^2 = 86
Am I on the right track?
You were using the wrong equation.
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Cheers,
Stan H.
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Answer by ccs2011(207)  (Show Source):
You can put this solution on YOUR website! You have the right idea with completing the square to find the vertex, however, your numbers are way off.
Also, do they provide the quadratic equation for you?
Because yours doesn't seem to model what they are looking for, it should be a downward parabola with a peak.
If you can provide the correct equation, I can help with the steps.
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