SOLUTION: 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.
Question 200863: 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).
Tickets= -0.2x^2+12x+11
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?
a. Opens down because the lead coefficient is negative
b. They increase to a maximum point and then decrease
c.
You can do your own arithmetic. Exclude the negative root -- you didn't start selling tickets before you started selling tickets.
d. Calculate the -coordinate of the vertex using . Calculate the value of the function at this value. Take the result of part c and divide by 2 to find the middle of your sale period, then calculate the value of the function at that value. The two should be very close. The vertex of a parabola that opens downward is a maximum.
