SOLUTION: Suppose you are an event coordinatorfor a large performance theater. One of the hottestnew Broadway musicals has started on tour, and your city is the first on the tour. You need t

Question 145536: Suppose you are an event coordinatorfor a large performance theater. One of the hottestnew Broadway musicals has started on tour, and your city is the first on the tour. You need to supply information aboutn 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 ticket sales for each day x.(x=1 is the day tickets go on sale). Tickets= -0.2x^2 + 12x + 11
a.)Describe what happens to ticket sales as time passes?
b.)Use the quadratic equation to determine the last day that tickets will be sold.(Note:write your answer in terms of number of days afterticket sales begin.)
c.)Will tickets peak or be at low during the middle of the sale? How do you know?
d.)After how many dayswill the peak or low occur?
e.)How many tickets will be sold on the day when the peak or low occurs?
f.)What is the point of the vertex? How does this number relate to your answersin parts d and f?
g.)How many solutions are there to the equation -.2x^2 + 12x + 11? How do you know?
h.)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?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You provide the manager with a Quadratic equation that models the expected ticket sales for each day x.(x=1 is the day tickets go on sale).
Tickets= -0.2x^2 + 12x + 11
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Graph:

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a.)Describe what happens to ticket sales as time passes?
They go up then down
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b.)Use the quadratic equation to determine the last day that tickets will be sold.(Note:write your answer in terms of number of days afterticket sales begin.)
Solve: -0.2x^2 + 12x + 11 = 0 for x to get x = 59
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c.)Will tickets peak or be at low during the middle of the sale? How do you know?
peak; look at the graph
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d.)After how many days will the peak or low occur?
30
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e.)How many tickets will be sold on the day when the peak or low occurs?
Find f(30) = 191
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f.)What is the point of the vertex? How does this number relate to your answersin parts d and f?
See the graph and your answers to d and f
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g.)How many solutions are there to the equation -.2x^2 + 12x + 11? How do you know?
two; it is a quadratic function
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h.)What do the solutions represent?
days when the number of tickets sold is zero
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Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
Yes, when x or y is negative.
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Cheers,
Stan H.

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