Question 175899
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?
Down; the negative on the x^2 term
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b. Describe what happens to the tickets sales as time passes?
They decrease.
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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.)
-0.2x^2 + 12x + 11 =0
x = [-12 +- sqrt(144- 4*-0.2*11)]/[-0.4]
x = [-12 +- sqrt(152.8)]/[-0.4]
x = [-12 +- 12.36]/[-0.4]
x = 60.9
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d. Will tickets peak or be at a low during the middle of the sale? How do you know? 
They will peak in the middle of sales because the graph opens down.
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e. After how many days will the peak or low occur? 
x = -b/2a = -12/[-0.4] = 30
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f. How many tickets will be sold on the day when the peak or low occurs?
Find f(30)
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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? 
(30,f(3))
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h. How many solutions are there to the equation ? How do you know? 
2, it's a quadratic
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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? 
I'll leave that to you.
If it's negative, it doesn't make sense.
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Cheers,
Stan H.