SOLUTION: 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 = -0.2x^2+12x+11
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-> SOLUTION: 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 = -0.2x^2+12x+11
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Question 141054: 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 = -0.2x^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?
e. After how many days will the peak or low occur?
f. How many tickets will be sold on the day when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e and f?
h. How many solutions are there to the equation ? How do 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?
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. (x=1 is the day tickets go on sale).
Tickets = -0.2x^2+12x+11
:
The best way to do this, is to make the actual graph of the equation
it should look like this:
:
:
a. Does the graph of this equation open up or down? How did you determine this?
Look at it
:
b. Describe what happens to the tickets sales as time passes?
You could say the sales increase, reach a peak, then decrease to 0
:
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 -0.2x^2+12x+11 = 0 using the quadratic formula:
The positive solution will be about approx x = 61. (60th day of ticket sales)
:
d. Will tickets peak or be at a low during the middle of the sale? How do you know?
Look at the graph
:
e. After how many days will the peak or low occur?
Look at the graph
Find the axis of symmetry: x = -b/(2a); a=-.2; b=12
:
f. How many tickets will be sold on the day when the peak or low occurs?
Find the vertex using the above x value
:
g. What is the point of the vertex? How does this number relate to your answers in parts e and f?
That is the max
:
h. How many solutions are there to the equation ? How do you know?
This equation has two solution, but only the positive solution makes sense
:
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?
