In Exercises 1–6, (a) state the values of a, b, and c in the given quadratic function
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Applied Calculus
- In Exercises 9–12, find a first- degree polynomial function P1 whose value and slope agree with the value and slope of f at x = c. Use a graphing utility to graph f and P1.arrow_forwardThe 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?arrow_forwardExercises 47 D–520: The graph of either a cubic, quartic, or quintic polynomial f(x) with integer zeros is shown. Write the complete factored form of f(x). (Hint: In Exercises 51 O and 52 O the leading coefficient is not +1.)arrow_forward
- In Exercises 12–20, find all zeros of each polynomial function. Then graph the function. 12. f(x) = (x – 2)°(x + 1)³ 13. f(x) = -(x – 2)(x + 1)? 14. f(x) = x - xr? – 4x + 4 15. f(x) = x* - 5x² + 4 16. f(x) = -(x + 1)° 17. f(x) = -6x³ + 7x? - 1 18. f(x) = 2r³ – 2x 19. f(x) = x - 2x² + 26x 20. f(x) = -x + 5x² – 5x – 3 %3D %3D %3! %3D %3!arrow_forwardIn 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.arrow_forwardIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. 2. f(x)=7x2 +9x4 3. g(x) = 7x5 - px3 + 1/5x 5. h(x) = 7x3 +2x2 + 1/x 7. f(x)=x1/2 -3x2 +5arrow_forward
- 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)arrow_forwardRead and understand the lessons on transforming and graphing quadratic functions on pages 26– 30 in PIVOT 4A Grade - 9 Mathematics Answer the following: I. Transform the quadratic function defined by y = ax2 + bx+ c into the form y = a(x-h)² + k. -1 --i-1 1. y = x2 – 6x – 3 2. y = 5x2 – 20x – 5arrow_forwardIn 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)arrow_forward
- For Exercises 23–24, use the remainder theorem to determine if the given number c is a zero of the polynomial. 23. f(x) = 3x + 13x + 2x + 52x – 40 a. c = 2 b. c = 24. f(x) = x* + 6x + 9x? + 24x + 20 а. с 3D —5 b. c = 2iarrow_forwardFor Exercises 69–84, find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) 69. f(x) = 8x – 42x + 33x + 28 (Hint: See Exercise 61.) 6x – x? (Hint: See Exercise 62.) 70. f(x) - 57x + 70 72. f(x) = 3x – 16x + 5x + 90x (Hint: See Exercise 64.) 2x + 11x - 63x? - 50x + 40 71. f(x) = (Hint: See Exercise 63.) - 138x + 36arrow_forwardIn Problems 33–44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rationalzeros of each polynomial function. Do not attempt to find the zeros.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage