Math117 Appendix F
Math117 Appendix F
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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 Tickets 2 02X2 12X 11 a Does the graph of this equation open up or down How did you determine this The graph opens downward because the lead coefficient O2 is a negative number b Describe what happens to the tickets sales as time passes At the beginning ticket sales increase but later they start to decrease 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 12 i 122 4 O21 1 x 2 O2 x 12i14488 04 x 12i1528 04 12i1236 x 04 x 121236 12 1236 or 04 04 x O9 or x 609 MAT 117 Reject x 903 because that is before tickets went on sale Note that we do not use partial days On day 60 the model predicts that there will be 11 tickets sold but on day 61 the model predicts that 12 tickets will be sold which is impossible The last day that tickets will be sold is 60 days after they initially went on sale d Will tickets peak or be at a low during the middle of the sale How do you know Ticket sales will peak Since the parabola opens downward from part a it has a maximum value e After how many days will the peak or low occur Using x b2a x 12 30days 2 02 Alternatively find the midpoint between the roots found in part c 09 609 x 2 30 f How many tickets will be sold on the day when the peak or low occurs Substitute x 30 into original model Tickets o2302 1230 1 1 O290036011 191 191 tickets are sold on the busiest day Q What is the point of the vertex How does this number relate to your answers in parts e and f The point is 30191 The 30 is the number of days it takes for sales to peak x and the 191 is the number of tickets sold on the 30th day h How many solutions are there to the equation 02362 12x 11 0 How do you know The equation has two solutions We know for two reasons 1 We found the two solutions in part c 2 The discriminant b24ac is 1528 a positive number 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 The solutions to the equation are the days when no tickets are expected to be sold One solution is 09 which is before tickets go on sale so this solution does not make sense and should be eliminated MAT 117 MAT 117
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