SOLUTION: Dear tutor, I am in Iraq about to fail my math class. Can you please assist with these problems? Suppose you are an event coordinator for a large performance theater. One of the

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Question 290255: Dear tutor, I am in Iraq about to fail my math class. Can you please assist with these problems?
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 = -0.2^2 + 12x + 11
In this equation, does the graph of the equation open up or down?
Describe what happens to the tickets sales as time passes?
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.
After how many days will the peak or low occur?



Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You forgot the x^2 in the first term which caused this equation to be a straight line rather than a parabola.

t= -0.2x^2 + 12x + 11
opens down - Notice the x^2 term is minus
This is a parabola like the St Louis Arch .
It rises then peaks and falls
The graph below doesn't show the arch because the numbers shown are too small
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.2x%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-0.2%2A11=152.8.

Discriminant d=152.8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+152.8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+152.8+%29%29%2F2%5C-0.2+=+-0.903074280724887
x%5B2%5D+=+%28-%2812%29-sqrt%28+152.8+%29%29%2F2%5C-0.2+=+60.9030742807249

Quadratic expression -0.2x%5E2%2B12x%2B11 can be factored:
-0.2x%5E2%2B12x%2B11+=+-0.2%28x--0.903074280724887%29%2A%28x-60.9030742807249%29
Again, the answer is: -0.903074280724887, 60.9030742807249. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.2%2Ax%5E2%2B12%2Ax%2B11+%29

The solutions tells when t is zero.
The peak will be -b/2a=-12/-2*.2=120/4=30
-b/2a is the x of the vertex and the axis of symmetry.
The peak occurs on the 30th day.
The last day is 60.9 or on the 61st day
And apparently some tickets were sold the day before tickets were sold.