SOLUTION: 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

Question 199430: 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?
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?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Can't help you unless you share the actual function, except in very general terms.

If the coefficient on the

term is positive, then the curve opens upward, otherwise it opens down. From the way part c is worded, I suspect it opens down -- otherwise, there wouldn't be a "last day"

With that presumption, the ticket sales will increase to a peak and then fall off (part b)

To answer part c, set the function equal to zero and then solve the quadratic. You would exclude any zero or negative root because the last day can't be the first day and the last day can't happen before the first day.

part d: see the answer to part b.

Given a quadratic function

, the vertex occurs at the x-coordinate

. That will answer part e.

Evaluate the function at the answer to part e, that is substitute that value for x in the function and calculate the value of the function to get part f.

The answers to e and f are the coordinates of the ordered pair representing the vertex.

for part h, I can't exactly say without looking at the actual function, however using the assumption I used for part c, the vertex is probably above the x-axis, hence the curve intersects the x-axis in two places -- hence two solutions.

Each solution represents a day when ticket sales are zero. A negative solution would not make sense in terms of what is going on. Of course ticket sales are zero at any time before you start selling them -- but knowing that isn't very helpful when trying to model the situation.

John

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