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).
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?
ans:
a) if this is a parabola it would open down.
b) since tickets sales would go up because of "hotness" of the show, but eventually it would go down.
c)I cannot explain since no equation was given to me
d) Peak; the parabola has a maximum point(since it opens down)
e) again I cannot give you this since no equation was given
f) same as e
g)Give me the equation and I shall explain and give the answer
Suppose you are a student at AXIA COLLEGE and you do your OWN home workQ!!
a. To determine whether the graph of the quadratic equation opens up or down, you need to examine the leading coefficient of the equation. If the leading coefficient is positive, then the graph opens up. If it is negative, then the graph opens down. Look at the quadratic equation provided and identify the coefficient in front of the x^2 term. If it is positive, the graph opens up; if it is negative, the graph opens down.
b. As time passes, the ticket sales will initially start off slowly and then increase gradually. Eventually, the sales will reach a peak and then start to decline until all the tickets are sold out. This is a typical pattern for many events and shows.
c. To determine the last day that tickets will be sold, you need to find the day when the ticket sales reach zero. Set the quadratic equation equal to zero and solve for the value of x. The resulting value of x will represent the last day when tickets will be sold.
d. The tickets will peak during the middle of the sale. This can be determined by noticing that the quadratic equation forms a symmetric curve, and the peak or low point (also known as the vertex) occurs in the middle.
e. To find out after how many days the peak or low occurs, you need to find the x-value of the vertex of the quadratic equation. The x-value of the vertex represents the number of days after ticket sales begin when the peak or low occurs.
f. Once you know the number of days when the peak or low occurs (the x-value of the vertex), you can substitute this value back into the quadratic equation to find the corresponding number of ticket sales on that day. This will give you the answer to how many tickets will be sold on the day the peak or low occurs.
g. The point of the vertex is the highest or lowest point on the graph of the quadratic equation. It represents the optimum number of ticket sales during a specific day after ticket sales begin. The x-value of the vertex corresponds to the day when the peak or low occurs, and the y-value represents the number of tickets sold on that day. Therefore, the number from the point of the vertex relates to the answers in parts e and f.