SOLUTION: Thanks Stan that was a great help. I was able to figure out that I had been using the wrong formula. I was able to answer a few more of the questions i and h. But I am stuck on que

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Question 177198: Thanks Stan that was a great help. I was able to figure out that I had been using the wrong formula. I was able to answer a few more of the questions i and h. But I am stuck on question d. and e. Should I be using the (b/2a)^2 then factor the left side and simplify the right?
1.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. ( is the day tickets go on sale).
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?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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.)
Determine when sales = zero:
-0.2x^2+12x+11 = 0
x = [-12 +- sqrt(144 -4*-0.2*11)]/[2*-0.2]
x = [-12 +- sqrt(152]/[-0.4]
Positive solution:
x = [-12 - 12.36]/[-.4]
x = [-24.36]/-0.4] = 60
Sales are 0 on day 60
Last day tickets will be sold will be day 59
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P.S. I made a typo on the earlier solution.
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d. It's a peak because the quadratic opens down.
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e Peak occurs when x = -b/2a = -12/(2*-0.2) = -12/-0.4 = 30
The number of sales that day is:
s(30) = -0.2(30)^2 + 12(30) + 11 = 191
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Cheers,
Stan H.