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
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The best way to do this, is to make the actual graph of the equation
it should look like this:
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{{{ graph( 300, 200, -20, 75, -20, 200, -0.2x^2+12x+11) }}}
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a. Does the graph of this equation open up or down? How did you determine this?
Look at it
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b. Describe what happens to the tickets sales as time passes?
You could say the sales increase, reach a peak, then decrease to 0
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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: {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
The positive solution will be about approx x = 61.  (60th day of ticket sales)
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d. Will tickets peak or be at a low during the middle of the sale? How do you know? 
Look at the graph
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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
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f. How many tickets will be sold on the day when the peak or low occurs?
Find the vertex using the above x value
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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
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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
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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?