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Question 625829: Please help!! I know that this has been answered before, but I cant find it answered with my equation. My numbers are different and I dont know how to convert the equations using my numbers. Please Please Please Help!!
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).
tickets = -0.3^2+6x+22
a. Does the graph of this equation open up or down? How did you determine this?
b. Describe what happens to the tickets sales as time passes.
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.
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?
f. How many tickets will be sold on the day when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?
h. How many solutions are there to the equation? How do you know?
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?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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).
tickets = -0.3x^2+6x+22
a. Does the graph of this equation open up or down? How did you determine this?
It opens downwards.
You can tell by looking at the coefficient associated with the x^2 term -- in this case it is -0.3. Since it is negative, it opens downward (if it was positive, it would open upwards).
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b. Describe what happens to the tickets sales as time passes.
Polynomials of degree two (which is the case), is a "quadratic". Knowing this, it is always in the shape of a parabola. So, as time passes it will initially rise, reaches a peak (at the vertex), and then falls as time passes.
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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.
tickets = -0.3x^2+6x+22
set "tickets" equal to zero and solve for x
0 = -0.3x^2+6x+22
applying the "quadratic formula" yields
x = {-3.17, 23.17}
you can throw out the negative solution (extraneous) leaving
x = 23.17
tickets sales will end on the 24th day
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d. Will tickets peak or be at a low during the middle of the sale? How do you know?
NO, Since the parabola opens downward, the peak will be at the highest point not the lowest.
e. After how many days will the peak or low occur?
at the axis of symmetry:
x = -b/(2a)
x = -6/(2(-0.3))
x = -6/(-0.6)
x = 10 days
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f. How many tickets will be sold on the day when the peak or low occurs?
plug part e answer into:
tickets = -0.3x^2+6x+22
tickets = -0.3(10)^2+6(10)+22
tickets = -0.3(100)+60+22
tickets = -30+60+22
tickets = 30+22
tickets = 52
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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?
vertex is at (10, 52)
h. How many solutions are there to the equation? How do you know?
From our answer in part c:
we had TWO solutions
x = {-3.17, 23.17}
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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?
represents when tickets sold was zero.
The negative answer doesn't make sense.
Only the positive answer makes sense.
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