Question 375874: I am having trouble wiyh my Appendix F. Can someone help me 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. ( is the day tickets go on sale).
Tickets = x2 - 6x + 16
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 x2 - 6x + 16? 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 Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, I'm sorry to hear that you're having trouble with your appendix but you really should see a doctor, it might be appendicitis.
But back to the problem:
Given the equation for expected ticket sales (T):
a) The graph opens up. You know (or should know) this because the coefficient of the  term is positive (+1). If it were negative, the graph would open down.
b) The number of tickets, T, first goes down until day 3 (x = 3), then it goes up.
c) There's no way to answer this question without first knowing how many tickets were for sale to begin with. This information was not provided.
d) Since the graph opens up, the vertex is a minimum and the tickets will be at a low, but whether this is at the middle of the sale cannot be determined since you have not provided the total number of tickets for sale.
e) The minimum (low) occurs at 3 days (x=3).
f) The number of tickets, T, sold at day 3 is 7 (T = 7 when x = 3).
g) The point of the vertex is (3, 7) and this is determined either from the graph or algebraically:
Find the x-coordinate by:
 Now plug this into the quadratic eqation to find y (or T in this problem)
 Evaluate.
The vertex is at (3, 7)
h) There are two solutions to the given quadratic equation. The number of solutions is equal to the highest power of the independent variable (x) which is 2 in this problem.
i) The solutions to this equation are not real numbers so they are meaningless.
 and 
The solutions are meaningless because the graph never intersects the x-axis indicating that the number of tickets sold never reaches zero.
In the graph, T (Expected number of tickets sold)is the vertical axis and x (Days after start of sale) is the horizontal axis.
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