mat 117 appendix F (brand new)
mat 117 appendix F (brand new)
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 x 1 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 It is open downward because the coe icient of x26 the quadratic equation is negative b Describe what happens to the tickets sales as time passes The sales will increase as the time increases reaches a maxima then decreases 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 Put number of tickets T 0 02 x2 12x110 2 ax bxc0 MAT 117 using the quadratic formula x bib2 4ac 2a a 02b12c11 124r 122 4 0211 2x 02 X Z 30 i 30 903 x30 30 903Vx3030 903 x 0 903Vx 60 903 x cannot be negative so we reject the value 0 903 therefore x 60 903 rounding o we get x 61 tickets sale become zero on 6 1 day d Will tickets peak or be at a low during the middle of the sale How do you know Ticket sale will maximize a pe ak at the middle of the sale this will be the vertex of the parabola this happens because it is a open downward parabola e After how many days will the peak or low occur Find the vertex of the parabola Vertex of the parabola could be found as The x coordinate x b 2 a b 96 2a 12 2 02 MAT117 230 Therefore peak occurs on 30th day f How many tickets Will be sold on the day when the peak or low occurs Y coordinate of the vertex will give the maximum ticket sale fl30 412302123011 L 18036011 L191 therefore maximum ticket sale 2 191 tickets g What is the point of the vertex How does this number relate to your answers in parts e and f The vertex is found at the point30l91 These numbers relate Z the answers E parts e f since they represent the x y coordinates 02x2 12xll 0 h How many solutions are there to the equation How do you know We can find the number of solution by nding the discriminant of the equation Dz 4C D122 411 02 D14488 l1528 Dgt0 therefore equation has two real solution this we can cross through part c 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 represent the number of days that tickets were on sale E this example The answers are 61 l The solutions 1 does not make sense Since MAT 117 1 cannot be an answer 3 a number of days we reject it MAT 117
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