Answer the following questions. Use Equation Editor when writing mathematical expressions or equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. You must show your work and/or justify your answer on ALL problems (even if it isn’t requested or the problem seems simple).

1.   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 can you determine this without looking at the graph? (3 pts)

b. Describe what happens to the tickets sales as time passes. Explain how you know this. (3 pts)

c. Use the quadratic formula to determine the last day that tickets will be sold. Show all work. (6 pts)

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? (4 pts)

e. After how many days will the peak or low occur? Show all work. (6 pts)

f. How many tickets will be sold on the day when the peak or low occurs? Show all work. (5 pts)

g. What are the coordinates for the vertex point? How does this number relate to your answers in parts e. and f? Explain your answer. (4 pts)

h. How many solutions are there to the equation? How is this determined without actually solving or graphing the equation? Show all work. (5 pts)

i. What do the solutions represent in terms of the scenario presented? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? (4 pts)