SOLUTION: Please help with this homework! Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your cit

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Question 457229: Please help with this homework!

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.
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?

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.6x%5E2%2B12x%2B11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A-0.6%2A11=170.4.

Discriminant d=170.4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+170.4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+170.4+%29%29%2F2%5C-0.6+=+-0.878112581387147
x%5B2%5D+=+%28-%2812%29-sqrt%28+170.4+%29%29%2F2%5C-0.6+=+20.8781125813871

Quadratic expression -0.6x%5E2%2B12x%2B11 can be factored:
-0.6x%5E2%2B12x%2B11+=+-0.6%28x--0.878112581387147%29%2A%28x-20.8781125813871%29
Again, the answer is: -0.878112581387147, 20.8781125813871. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.6%2Ax%5E2%2B12%2Ax%2B11+%29

opens down because of - coefficient of x^2