Question 366785: 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. What is the number of tickets sold on the 10th day? The 20th day? The 40th day? The 50th day?
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. After how many days will the maximum or minimum occur?
e. How many tickets will be sold on the day when the maximum or minimum occurs?
f. What are the coordinates of the vertex? How does this number relate to your answers in parts d and e?
g. How many solutions are there to the equation ? How do you know?
h. What do the solutions represent? Explain.