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Reminder • Quiz corrections for Ch. 2 due this Thursday. HWQ For the function find the following: 5 x3 15 x 2 20 x f x x 2 x 12 State asymptotes as equations of lines and intercepts as ordered pairs. a) Vertical Asymptotes and holes b) Horizontal (or) Slant Asymptotes c) X-intercepts d) Y-intercepts e) Domain 2.8 Exploring Data: Quadratic Models Students will classify scatter plots. Students will use scatter plots and a graphing utility to find quadratic models for data. Students will choose a model that best fits a set of data. Example 1 Decide whether each data set would best be modeled by a linear model or a quadratic model. • a) (1, 3), (2, 5), (4, 6), (6, 8), (8, 9), (10, 10), (12, 13) a ) linear model • b) (2, 1), (4, 2), (6, 4), (8, 7), (9, 10), (11, 15), (13, 20) b) quadratic model Enter both sets of data into a graphing utility and display the scatter plots. Example 2 The following table gives the mileage y, in miles per gallon, of a certain car at various speeds x (in miles per hour). a) Use a graphing utility to create a scatter plot of the data. b) Use the regression feature of a graphing utility to find a quadratic model that best fits the data. c) Use the model to predict the speed that gives the greatest mileage. Speed, x Mileage, y 10, 21.3 45, 31.9 b) y .012 x 2 .948 x 12.285 15, 23.7 50, 29.5 20, 25.9 55, 27.6 c) Maximum @ 39.5,31 25, 27.6 60, 25.3 Speed that gives the greatest 30, 29.4 65, 23.0 mileage is 39.5 mph. 35, 31.0 70, 20.0 40, 31.7 P 0.132t 2 1.901t 6.872 The following table gives the monthly normal precipitation P (in inches) for San Francisco, California. a) Use a graphing utility to create a scatter plot of the data. Let t represent the month with t=1 corresponding to January. b) Use the regression feature of a graphing utility to find a quadratic model that best fits the data. c) Graph the model with the scatter plot from part b. d) Use the model to predict the precipitation in San Francisco on September 15th. Month t Precip. P Month t Precip. P January 4.45 July .03 February 4.01 August .07 March 3.26 September .20 April 1.17 October 1.04 May .38 November 2.49 June .11 December 2.89 Polynomial application • An open box is to be made from an 8x11 piece of cardboard by cutting equal squares with sides of length x from the corners and turning up the sides. • a) find an expression for the volume of the box as a function x. • b) find the x-value for which V(x) is a maximum. Polynomial application • Find two positive real numbers whose product is a maximum and where the sum of the first and three times the second is 42. Polynomial application You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What dimensions produce the maximum area? What is the maximum area that you can enclose? You Try: A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals. What dimensions should be used so that the enclosed area will be a maximum? Homework • Chapter 2 Practice test (Pg 99 in solution manual) – (Pg 533 Answers in solution manual)