Question 626566: 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. (x=1 is the day tickets go on sale).
Does the graph of this equation open up or down? How did you determine this?
As time passes, explain how the tickets sales change. Will ticket sales peak or be at a low during the middle of the time period they are on sale? How do you know?
After how many days will the peak or low occur? How many tickets will be sold on the day when the peak or low occurs? Explain how you arrived at your answer.
How many solutions are there to the equation ? (Do not solve the equation in this step.) Explain how you arrived at your answer.
Use the quadratic formula to solve the quadratic equation in part d. Write the answer in decimal form and round to the nearest whole number. Is there a solution that does not make sense? If so, in what way does the solution not make sense?
When should you expect to stop selling tickets for this musical? Explain how you arrived at your answer.