In Exercises 130–133, use a graphing utility to graph the functions y, and y2. Select a viewing rectangle that is large enough to show the end behavior of y2. What can you conclude? Verify your conclusions using polynomial multiplication. 130. yı = (x - 2)² y2 = x2 – 4x + 4 131. yı = (x – 4)(x² y2 = x - 7x2 + 14x – 8 132. yı = (x – 1)(x + x + 1) y2 = x – 1 133. yı = (x + 1.5)(x – 1.5) y2 = x? – 2.25 3x + 2)
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- In Exercises 17–27, use the vertex and intercepts to sketchthe graph of each quadratic function. Give the equation of the parabola’s axis of symmetry. Use the graph to determine the function’s domain and range. 23. f(x)=2(x+2)2 -1 25. f(x)=4-(x-1)2 27. f(x)=x2 -2x-3In Exercises 47–50, determine the x-intercepts of the graph of each quadratic function. Then match the function with its graph, labeled (a)-(d). Each graph is shown in a [-10, 10, 1] by [-10, 10, 1] viewing rectangle. 47. у 3D х2 -бх + 8 48. y = x? – 2r – 8 49. y = x² + 6x + 8 50. y = x² + 2x – 8 а. b. C. d.In Exercises 39–44, an equation of a quadratic function is given. a. Determine, without graphing, whether the function has a minimum value or a maximum value. b. Find the minimum or maximum value and determine where it occurs. c. Identify the function's domain and its range. 39. f(x) = 3x – 12x – 1 41. f(x) = -4x² + &r – 3 43. f(x) = 5x? - 5x 40. f(x) = 2x? – &r – 3 42. f(x) = -2r² – 12x + 3 44. f(x) = 6x - 6x %3D %3D %3D
- In Exercises 73–74, use the graph of the rational function to solve each inequality. flx) = + 1 [-4, 4, 1] by [-4, 4, 1] 1 1 73. 4(x + 2) 4(x – 2) 74. 4(x + 2) 4(x - 2)The Mauna Loa Observatory in Hawaii records the carbon dioxide concentration y (in parts per million) in Earth’s atmosphere. The January readings for various years are shown in Figure . In the July 1990 issue of Scientific American, these data were used to predict the carbon dioxide level in Earth’s atmosphere in the year 2035, using the quadratic model y = 0.018t2 + 0.70t + 316.2 (Quadratic model for 1960–1990 data) where t = 0 represents 1960, as shown in Figure a. The data shown in figure b represent the years 1980 through 2014 and can be modeled by y = 0.014t2 + 0.66t + 320.3 (Quadratic model for 1980–2014) data where t = 0 represents 1960. What was the prediction given in the Scientific American article in 1990? Given the second model for 1980 through 2014, does this prediction for the year 2035 seem accurate?Exercises 103–110: Let the domain of f(x) be [-1,2] and the range be [0, 3 ]. Find the domain and range of the following. 103. f(x – 2) 104. 5/(x + 1) 105. -/(x) 106. f(x – 3) + 1 107. f(2x) 108. 2f(x – 1) 109. f(-x) 110. -2/(-x)
- In Exercises 31–32, each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values. S3x + 5 ifx 0 31. f(x) = а. f(-2) b. f(0) с. f(3) d. f(-100) + f(100)Exercises 15-20: Identify the vertex and leading coeffi- cient. Then write the expression as f(x) = ax² + bx + c. 15. f(x) = -3(x = 1)² + 2 16. f(x) = 5(x + 2)² – 5 17. f(x) = 5 – 2(x – 4)² 18. f(x) = (x + 3)² – 5 19. f(x) = (x + 5)² - } 20. f(x) = -5(x – 4)²Questlon Enter a quadratic function after changlng from vertex form, y = a(x-h)+k, to standard form, y =ax2 +bx +c. y=-4x-3)2+3 The standard form of y = -4(x- 3)+3 is y =
- Plot the points of the graph of f(x)=-(x-5)^2+5 that correspond to x-values of 3 and 4. Then plot the vertex and the reflection of these points in the axis of symmetry.Describe the transformation of the graph of the parent quadratic function to the graph of f(x)=-4(x+1)^2. The identify the vertexExercises 73–80, find the difference quotientand simplify your answer.73. f(x) = x2 − 2x + 4, f(2 + h) − f(2)h , h ≠ 074. f(x) = 5x − x2, f(5 + h) − f(5)h , h ≠ 075. f(x) = x3 + 3x, f(x + h) − f(x)h , h ≠ 076. f(x) = 4x3 − 2x, f(x + h) − f(x)h , h ≠ 077. g(x) = 1x2, g(x) − g(3)x − 3 , x ≠ 378. f(t) = 1t − 2, f(t) − f(1)t − 1 , t ≠ 179. f(x) = √5x, f(x) − f(5)x − 5 , x ≠ 580. f(x) = x23 + 1, f(x) − f(8)x − 8 , x ≠ 8