SOLUTION: 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
Question 310424: 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=-0.3x^2+10x+12
Does the graph of this equation open up or down? Explain how you determine this.
The graph of this equation goes down because -0.3<0.
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. Show work!
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? Explain how you know.
e. After how many days will the peak or low occur? Show work!
f. How many tickets will be sold on the day when the peak or low occurs? Show work!
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f? Explain.
h. How many solutions are there to the equation ? Explain how you know.
i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? Explain.
You can put this solution on YOUR website! 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=-0.3x^2+10x+12
:
a. Does the graph of this equation open up or down? Explain how you determine this.
The graph of this equation goes down because -0.3<0.
:
b. Describe what happens to the tickets sales as time passes.
Easy to see if we plot a graph of the equation y = -0.3x^2 + 10x + 12
you can see it gradually reaches max sales of about 95 tickets on the 16th day
then drops off to 0 on day 34
:
c. Use the quadratic equation to determine the last day that tickets will be sold.
in this equation a=-.3; b=10; c=12
:
:
the positive solution (negative solution does not make sense
x =
x = 34.5
Write your answer in terms of the number of days after ticket sales begin.
last day is 34 when 0 tickets are sold
:
:
Note: you should be able to answer the rest of the questions by finding the
axis of symmetry; x = -b/(2a), then find the vertex (max) by substituting that value in original equation
:
d. Will tickets peak or be at a low during the middle of the sale? Explain how you know.
e. After how many days will the peak or low occur? Show work!
f. How many tickets will be sold on the day when the peak or low occurs? Show work!
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f? Explain.
h. How many solutions are there to the equation ? Explain how you know.
i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? Explain.
