SOLUTION: Can someone tell me if I did these right. If not can someone please help me with these problems PLEASE. Suppose you are an event coordinator for a large performance theater. One

Question 371849: Can someone tell me if I did these right. If not can someone please help me with these problems PLEASE.
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= -0.4x^2+20x+122.1
a. Does the graph of this equation open up or down? How did you determine this?
Downward, coefficient of the squared term is negative
b. What is the number of tickets sold on the 10th day? The 20th day? The 40th day? The 50th day?

T (10)= 182
T (20) = -0.4*(20) ^2+20*(20)+122.1
T (20) = -0.4*(400) +400+122.1
T (20) = -160+522.1
T (20) = 362.1
T (20) = 362
T (40) = -0.4*(40) ^2+20*(40) +122.1
T (40) = -0.4*1600+800+122.1
T (40) = -640+922.1
T (40) = 282.1
T (40) = 282
T (50) = -0.4*(50) ^2+20*(50) +122.1
T (50) = -0.4*2500+1000+122.1
T (50) = -1000+1122.1
T (50) = 122.1
T (50) = 122

c. Use the quadratic equation to determine the last day that tickets will be sold.
x = -5.5 and x = 55.55 the last day tickets will be sold

Note. Write your answer in terms of the number of days after ticket sales begin.
d. After how many days will the maximum or minimum occur?
55.55 - 60.05/2 = 25.525

e. How many tickets will be sold on the day when the maximum or minimum occurs?
374
f. What are the coordinates of the vertex? How does this number relate to your answers in parts d and e? 55
g. How many solutions are there to the equation ? How do you know?
2
h. What do the solutions represent? Explain.

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
a) Correct!
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b)

All of the other values are correct.
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c)Not sure what x=-5.5 and x=55.55 are??
The last day tickets will be sold is the last day that .

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d) The quadratic function, , has a maximum at

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e)

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f) The maximum occurs at the vertex.
(,)
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