# Y 4 2 o x 2 4 2 2 6 4 f x g x 10 vertex 3 2 axis of

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y 4 2 O x 2 4 2 2 6 4 f ( x ) g ( x ) 10. vertex ( - 3, 2), axis of symmetry x = - 3, maximum y = 2, domain ( - Ŭ¶ Ŭ·¶ TCPIG µ - Ŭ¶ ¸· 12. f ( x ) = 3 __ 4 ( x - 2) 2 + 1 14. g ( x ) = ( x - 2) 2 - 4 16. vertex (3, 6), y -intercept (0, 15) y 16 12 8 4 O x 4 8 8 4 enVision Algebra 2 | 11 | Selected Answers
Selected Answers Topic 2 PearsonRealize.com 18. y = x 2 - 3 x + 7 20. Answers may vary. Sample: Calculate the vertex to find the maximum height of the ball. You can use the vertex to find the horizontal distance from the starting point and multiply by 2 to find the total distance. 22. x = - 3 or x = 9 24. x = - 1.5 or x = 0.5 26. x < - 5 or x > 6 28. x - 6 30. 13 - i 32. 3 __ 2 - 1 __ 2 i 34. They did not change i 2 VQ Ũ±¹ µ¸ Ũ ² i )(4 + i ) = ±± Ũ ±º i 36. ( x - 8) 2 = 28 38. x = 12 ± ū ____ 226 40. x = 2 ± ū ___ 41 ____ 2 42. 5.04 seconds; The other root is negative, which is not an appropriate value for this situation. 44. x = 8 ± 2 ū ___ 10 46. x = 9 ± ū ___ 71 _______ 2 48. 2 real solutions 50. k = ± 8 52. below 25 kilometers per hour and above 79 kilometers per hour 54. 0 y 8 6 4 2 O x 1 2 1 2 56. ( - 1, 6), (0, 7) enVision Algebra 2 | 12 | Selected Answers
Selected Answers Topic 3 PearsonRealize.com Lesson 3-1 2. Allie did not write the polynomial function in standard form; instead, she said the exponent of the first term was the degree of the polynomial. The degree is 6. 4. For a polynomial function with an even degree, as x - and x + , y -values either both approach + or both approach - . If the leading coefficient is positive, both ends approach + . If negative, both ends approach - . A polynomial function with an odd degree has end behavior for positive and negative x in opposite directions. If the leading coefficient is positive, as x - , y , and as x + , y + . If the leading coefficient is negative, the end behavior is in the opposite direction. 6. 4 8. As x - , y + . As x + , y + . 10. x = - 4, x = - 2, x = 1, x = 3 12. approximately ( - 0.5, 28) 14. f ( x ) = - 2 x 5 + 2 x 4 - 2 x 3 + x 2 - x + 1; The polynomial function must have a negative leading coefficient and an odd degree because of the end behavior. The function must have a degree of at least 5 because there are 6 terms. The last term of the function is 1 because the y -intercept is (0, 1). y O x 4 2 4 2 4 2 4 16. Check students’ graphs. Sample: y O x 4 2 4 2 4 2 4 2 y O x 4 2 4 2 1 2 1 y O x 4 2 4 2 4 2 4 2 18. f ( x ) = 2 x 5 + x 4 + 5 x 3 - 3 x 2 + x - 6; 5; 6; 2 20. f ( x ) = x 4 - x 3 + 5 x 2 + 9 x + 12; 4; 5; –1 22. The leading coefficient, 7, is positive, so the graph opens upward. The degree is 4, which is even, so the end behaviors are the same. As x becomes infinitely positive or negative, the y -values approach + . enVision Algebra 2 | 13 | Selected Answers
Selected Answers Topic 3 PearsonRealize.com 24. zeros: x = - 3, x = - 1, x = 2; turning points between - 3 and - 1, between - 1 and 2 y O x 4 4 2 8 8 4 26. y O x 4 4 20 10 10 28. a. f ( x ) = 4 x 3 - 38 x 2 + 88 x b. reasonable domain: 0 < x < 4 y O x 4 6 2 2 20 20 40 60 c. x -intercepts: 0, 4, and 5.5; 0 and 4 represent the side lengths of the cut squares that will result in a box with 0 volume. The intercept at 5.5 is not meaningful, because it is not possible to cut two 5.5-inch corners from an 8-inch side. d. About 1.5 in. will create a box with a volume of about 60 in.