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
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-> 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
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Question 478425: 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.
(x = 1 is the day tickets go on sale).
Tickets = -0.6x2 + 12x + 11
Does the graph of this equation open up or down?
How did you determine this?
Describe what happens to the ticket sales as time passes.
Use the quadratic formula to determine the last day that tickets will be sold.
Hint: Write your answer in terms of the number of days after ticket sales begin and you can’t have partial days. -0.6x^2+12x+11=0
Will tickets peak or be at a low during the middle of the sale?
How do you know?
After how many days will the peak or low occur?
Hint: Use the axis of symmetry formula.
How many tickets will be sold on the day when the peak or low occurs?
Hint: Substitute your value from question 7 into the original quadratic equation.
What are the coordinates of the vertex?
How did you determine this?
How many solutions are there to the original quadratic equation given in question 3?
How do you know?
You can put this solution on YOUR website! -0.6x2 + 12x + 11
a. Does the graph of this equation open up or down? How did you determine this? (5pts)
DOWN - because the coefficient of the highest power term is negative.
How did you determine this?
.
B . Number of ticket sales goes down to zero.
c. 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.)
Solve E(x) = 0 for "x>0".
E(x) = -0.2 X^2 + 12 x + 11
Find the roots of the equation by quadratic formula
-b/2a= 30
a= -0.2 b= 12 c= 11
b^2-4ac= 144 - 8.8
b^2-4ac= 152.8 = 12.36
x1=( -12 + 12.36 )/ -0.4
x1= -0.9 - 8/9
x2=( -12 -12.36 ) / -0.4
x2= 60.9 60 8/9
Take the positive solution - The sale goes down to 0 on the day 61
The x co-ordinate of the parabola is -b/2a = 30
The peak will occur after about 30 days
Plug value of x co-ordinate of vertex in the equation
y= -180 + 360 + 11
y= 191
191 Tickets will be sold when the sale reaches the peak.
The x co-ordinate of the parabola is -b/2a
plug the vakue of x in the equation to get the y co-ordinate of the vertex. Vertex ( 30 , 191 )
