CSU - Dominguez hills
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Date Created: 11/16/15
Axia College Material Appendix F Ticket Sales Living in or near a metropolitan area has some advantages Entertainment opportunities are almost endless in a major city Events occur almost every night from sporting events to the symphony Tickets to these events are not available long and can often be modeled by quadratic equations Application Practice Answer the following questions Use Equation Editor to write mathematical expressions and equations First save this file to your hard drive by selecting Save As from the File menu Click the white space below each question to maintain proper formatting 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 x 1 is the day tickets go on sale a d Tickets 2 02X2 12X 11 Does the graph of this equation open up or down How did you determine this The graph opens down because the coefficient of the highest power term is negative Describe what happens to the tickets sales as time passes The ticket sales will start off slow and continue to rise for 30 days and then they will start to slow down until there is no longer a demand for the tickets Use the quadratic equation to determine the last day that tickets will be sold 0 02Xquot212X11 Multiply by 5 X2 60X 55 0 Quadratic formula x b sqrt b2 4ac 2a x 60 sqrt 602 4552 x 60903 or 0903 The tickets will sell for 61 day the 61St day being the last Note Write your answer in terms of the number of days after ticket sales begin Will tickets peak or be at a low during the middle of the sale How do you know MAT117 The vertex of the parabola is 12 202 30 Since 30 is the halfway point of 60 the peak will be during the middle of the sale After how many days will the peak or low occur About 30 days into the sales How many tickets will be sold on the day when the peak or low occurs 02302 1230 11 02900 360 11 180 360 11 191 191 tickets will be sold What is the point of the vertex How does this number relate to your answers in parts e and f The vertex is at 30191 The x coordinate is the day that the most were sold The y coordinate is the number of tickets How many solutions are there to the equation 02352 12x 11 0 How do you know There are two solutions because b24ac is positive 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 The solutions are the days when 0 tickets are sold The negative solution 0903 doesn39t make sense because that would be prior to when the tickets went on sale 4040 POINTS MAT117
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