f(x) = x2(x – 2x + 10) A. 0 B. 1 C. –1 D. –2 ____ 7. Determine the number of turning points of this polynomial function: f(x) = x2 – 5x – 1 A. 0 B. 1 C. 2 D. 3 ____ 8. Determine the equation of this polynomial function: A. f(x) = –x2 – 3x – 1 B. g(x) = x2 – 2x + 1 C. h(x) = –x3 – 2x2 + 1 D. j(x) = x3 + 2x ____ 9. Determine the equation of this polynomial function: A. f(x) = –x2 – 3x – 1 B. g(x) = x2 – 2x + 1 C. h(x) = –x3 – 2x2 + 1 D. j(x) = x3 + 2x ____ 10. Fill in the blanks to describe the end behaviour of this polynomial function: The curve extends from quadrant ____ to quadrant ____. A. II; I B. II; IV C. III; I D. III; IV ____ 11. The distance a marathon runner covers can be modelled by the function d(t) = 153.8t + 86 where d represents the distance in metres and t represents the time in minutes. Approximately how far has she run after the first hour?
C. 20 D. 0 ____ 16. Determine the equation of the linear regression function for the data. x 1 2 3 4 5 6 y 84 155 241 310 405 478 A. y = 79.7x – 0.07 B. y = 78.1x – 1.07 C. y = 79.7x + 0.07 D. y = 78.1x + 1.07 ____ 17. The path of a shot put thrown at a track and field meet is modelled by the quadratic function h(d) = –0.048(d2 – 20.7d – 26.28) where h is the height in metres and d is the horizontal distance in metres. Determine the height of the discus when it has travelled 10 m horizontally. A. 6.2 m B. 6.4 m C. 6.6 m D. 6.8 m ____ 18. Determine the equation of the quadratic regression function for the data. x 1 2 3 4 5 y 100.8 101.3 101.5 100.9 99.8 A. y = –0.3x2 + 1.5x + 99.6 B. y = –1.3x2 + 0.5x + 99.6 C. y = –0.5x2 + 1.3x + 99.6 D. y = –1.5x2 + 0.3x + 99.6 ____ 19. Determine the equation of the cubic regression function for the data. x 2 4 7 10 12 13 17 19 y 135 120 105 102 99 88 78 47 A. y = 0.05x3 – 1.5x2 – 16x + 162.5 B. y = –0.05x3 + 1.5x2 – 16x + 162.5 C. y = 0.05x3 + 1.5x2 + 16x – 162.5
D. y = –0.05x3 + 1.5x2 + 16x – 162.5 ____ 20. Determine the equation of the cubic regression function for the data. x 0 2 3 3 6 8 11 12 12 y 18.5 26.7 31.3 32.8 41.5 45.0 48.3 47.6 49.1 A. y = 1.4x3 + 0.2x2 – 5.1x + 18.3 B. y = –1.4x3 + 0.2x2 + 5.1x + 18.3 C. y = 1.4x3 – 0.2x2 – 5.1x + 18.3 D. y = –1.4x3 – 0.2x2 + 5.1x + 18.3 Short Answer 1. What is the degree of a linear function? 2. Determine the degree of this polynomial function: 3. Determine the degree of this polynomial function: f(x) = x2 – 5x + 1 4. Determine the degree of this polynomial function: f(x) = 104 – x2 + x 5. Determine the leading coefficient of this polynomial function: f(x) = x2 – 5x + 1 6. Determine the leading coefficient of this polynomial function: f(x) = 104 – x2 + x
19. Use quadratic regression to interpolate the value of y when x = 0. Round your answer to the nearest tenth. x –5 –3 –2 1 3 4 7 y 1.8 1.1 0.9 1.5 2.5 3.8 8.6 20. Use regression to extrapolate the value of y when x = 50. Round your answer to the nearest whole number. x 5 10 15 20 25 30 35 40 y 211 236 255 258 264 267 276 291 Problem 1. Determine the following characteristics of the polynomial function f(x) = x3 – 8x2 – 3. Show your work. • number of possible x-intercepts • y-intercept • end behaviour • domain • • number of possible turning points 2. Determine the following characteristics of the polynomial function f(x) = –5(3 – 2x)(x + 1). Show your work. • number of possible x-intercepts • y-intercept • end behaviour • domain • • number of possible turning points 3. Determine the following characteristics of the polynomial function f(x) = –5(x – 1)(x2 + 4). Show your work. • number of possible x-intercepts • y-intercept • end behaviour • domain • range • number of possible turning points 4. Identify the correct polynomial function for this graph. Justify your reasoning. i) y = –x + 1 iv) y = – – x