Living in or near a metropolitan area has some advantages. Entertainment opportunities are almost endless in a major city. Events occur almost every night, from sporting events to the symphony. Tickets to these events are not available long and can often be modelled by quadratic equations.
1. Assume you are the event coordinator for a large performance theatre. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You are required to supply information about projected ticket sales to box office manager. Box office manager uses this information to expect staffing requirements till the tickets sell out. You give a quadratic equation to manager which 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 find out this?
b. Explain what happens to tickets sales as time passes.
c. Use the quadratic equation to find out the last day that tickets would be sold.
Note. Write the answer in terms of the number of days after ticket sales begin.
d. Would tickets peak or be at a low during middle of the sale? How do you know?
e. After how many days would the peak or low occur?
f. How many tickets would 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 signify? Is there a solution which does not make sense? If so, in what ways does the solution not make sense?