Answers to Odd Problems

Answers to Odd Problems Chapter 5 Section 5.1 1) 𝑥 = ±4 3) 𝑏 = ±7𝑖 5) 𝑚 = ±7√2 7) 𝑥 = ±5𝑖√3 9) x = 8, -2 11) x = 6, -1 13) 𝑥 = 4 ± 5√6 15) 𝑥 = 21) C= 9 (x +3)2 29) 𝐶 = 9 23) C = 25 (y+5)2 9 31) 𝐶 = 4 17) 𝑥 = 20 3 ,− 22 3 19) 𝑥 = −2±3√21 3 25) C=4 27) C=49 (b-2)2 (x-7)2 33) 𝐶 = 49 (𝑥 − ) (𝑎 − 2 41) a= -12, 2 49) a = 6 ± 3√6 57) 𝑥 = −3±𝑖√11 2 Section 5.2 1a) x =-6,2 3b) 𝑦 = −5 ± √30 5 11) 𝑤 = 1, − 2 19) 𝑡 = −5±√89 4 27) x = -4, 5 121 2 1 (𝑏 + ) 4 21) 𝑥 = 29) 𝑥 = 47) x = −1 ± √7 55) 𝑥 = −4 ± 2𝑖 45) x = 7,1 53) 𝑏 = −3 ± 2√5 −3±√19 3 61) 𝑥 = 4,-1 2 1b) x = -6, 2 5) y = -8,2 13) 𝑧 = 39) x = -7,1 1 2 ) 43) a= -5, 15 51) 𝑥 = −3 ± √14 59) 𝑥 = (𝑥 + 2) 37) 𝐶 = 16 4 11 2 2 3 2 (𝑥 + 3)2 35) 𝐶 = 4 7 2 6±5𝑖√3 3a) 𝑦 = −5 ± √30 9) 𝑦 = 1 ± 𝑖√5 1c) x = -6,2 7) x = -3 2±𝑖√5 15) 𝑦 = 3 −5±√37 23) 𝑦 = 2 1±√13 31) 𝑦 = 3 2±√2 17) y = -6,1 3 −3±√41 25) x=5, -3 8 1±√17 2 Section 5.3 1) f(x) = x2 y 6 x f(x) 2 4 1 1 0 0 -1 1 -2 4 Vertex (0,0) 5 4 3 2 1 x -6 -5 -4 -3 -2 -1 (0,0) 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 92 Answers to Odd Problems Section 5.3 3) k(x) = x2 + 4 x 2 1 0 -1 -2 Vertex (0,4) 5) n(x) = x2 – 6 x 2 1 0 -1 -2 k(x) 8 5 4 5 8 y 10 8 6 4 (0,4) 2 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -6 n(x) -2 -5 -6 -5 -2 y 6 5 4 3 2 1 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 Vertex (0,-6) -3 -4 -5 -6 (0,-6) 7) f(x) = 3x2 – 4 y 6 x 2 1 0 -1 -2 f(x) 8 -1 -4 -1 8 5 4 3 2 1 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 -3 -4 (0,-4) -5 -6 Vertex (0,-4) 93 Answers to Odd Problems Section 5.3 9) b(x) = -5x2 + 12 x -2 -1 0 1 2 Vertex (0, 12) y b(x) -8 7 12 7 -8 14 (0,12) 12 10 8 6 4 2 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -6 11) m(x) = -2x2 +1 x 2 1 0 -1 -2 m(x) -7 -1 1 -1 -7 y 6 5 4 3 2 (0,1) 1 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 3 4 6 -1 -2 Vertex (0,1) -3 -4 -5 -6 13) f(x) = (x – 2)2 x 4 3 2 1 0 f(x) 4 1 0 1 4 y 6 5 4 3 2 1 x -6 -5 -4 -3 -2 -1 1 -1 Vertex (2,0) Axis of symmetry x = 2 2 (2,0) 5 6 -2 -3 -4 -5 -6 94 Answers to Odd Problems Section 5.3 15) m(x) = (x – 1)2 x 3 2 1 0 -1 Vertex (1,0) Axis of symmetry x=1 m(x) 4 1 0 1 4 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 y x 1 (1,0) 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 17) n(x) = (x+3)2 x -1 -2 -3 -4 -5 y n(x) 4 1 0 1 4 6 5 4 3 2 1 x -6 Vertex (-3,0) Axis of symmetry x = -3 -5 -4 -3 (-3,0) -2 -1 1 2 3 4 5 -1 -2 -3 -4 -5 -6 95 6 Answers to Odd Problems Section 5.3 19) f(x) = 3(x – 2)2 x 4 3 2 1 0 y f(x) 12 3 0 3 12 6 5 4 3 2 1 x -6 -5 -4 -3 -2 -1 1 2 -1 Vertex (2,0) Axis of symmetry x = 2 3 (2,0) 4 5 6 -2 -3 -4 -5 -6 21) b(x) = −1 2 (x – 5)2 x 7 6 5 4 3 b(x) -2 -1/2 0 -1/2 -2 y 6 5 4 3 2 1 (5,0) -6 -5 -4 -3 -2 -1 1 2 3 4 5 x 6 7 8 9 10 -1 -2 Vertex (5,0) Axis of symmetry x = 5 -3 -4 -5 -6 2 23) 𝑟(𝑥) = 5 (𝑥 + 1)2 x 1 0 -1 -2 -3 Vertex (-1,0) Axis of symmetry x = -1 r(x) 8/5 2/5 0 2/5 8/5 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 (-1,0) y x 1 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 96 Answers to Odd Problems Section 5.3 25) f(x) = (x – 3)2 + 4 x 5 4 3 2 1 y f(x) 8 5 4 5 8 10 8 6 4 (3,4) 2 Vertex (3,4) Axis of symmetry x = 3 Vertex is a minimum point Minimum y value is y = 4 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 -2 -4 -6 27) h(x) = 2(x+3)2 – 4 x -1 -2 -3 -4 -5 y h(x) 4 -2 -4 -2 4 10 8 6 4 2 Vertex (-3, -4) Axis of Symmetry x = -3 Vertex is a minimum point Minimum y value y = -4 x -6 -5 -4 -3 -2 -1 6 7 8 9 -2 -4 (-3,-4) -6 97 10 Answers to Odd Problems Section 5.3 1 29) g(x) = 2 (𝑥 + 4)2 − 6 x g(x) -2 -4 -3 -5.5 -4 -6 -5 -5.5 -6 -4 Vertex (-4, -6) Axis of symmetry x = -4 Vertex is a minimum point Minimum y value y = -6 y 10 8 6 (-4,6) 4 2 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -2 -4 -6 31) m(x) = -2x2 + 3 x 2 1 0 -1 -2 y m(x) -5 1 3 1 -5 10 8 6 4 (0,3) 2 x Vertex (0,3) Axis of symmetry x = 0 Vertex is a maximum point Maximum y value y = 3 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -2 -4 -6 98 Answers to Odd Problems Section 5.3 33) x f(x) -3 -3 -4 -9/4 -5 -2 -6 -9/4 -7 -3 Vertex (-5, -2) Axis of symmetry x = -5 Vertex is a maximum point Maximum y-value y = -2 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 (-5,-2) -3 -2 -1 -1 y x 1 2 3 4 5 4 5 6 7 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 35) b(x) = 2(x+3)2 + 4 y 10 x b(x) -1 12 -2 6 -3 4 -4 6 -5 12 Vertex (-3, 4) Axis of symmetry x = -3 Vertex is a minimum point Minimum y value y = 4 8 6 4 (-3,4) 2 x -6 -5 -4 -3 -2 -1 1 2 3 8 9 10 -2 -4 -6 99 Answers to Odd Problems Section 5.3 37) f(x) x2 + 6x + 5 y 10 x -1 -2 -3 -4 -5 f(x) 0 -3 -4 -3 0 8 6 4 2 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -2 Vertex (-3, -4) Axis of symmetry x = -3 Vertex is a minimum point Minimum y value y = -4 -4 (-3,-4) -6 39) x k(x) 4 2 3 -1 2 -2 1 -1 0 2 Vertex (2,-2) Axis of symmetry x =2 Vertex is a minimum point Minimum y value, y = -2 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 y x 1 2 3 4 5 6 7 8 9 (2,-2) 100 Answers to Odd Problems Section 5.3 41) f(x) = 2x2 + 8x – 3 x f(x) -4 -3 -2 -9 -2 -11 -1 -9 0 -3 Vertex (-2, -11) Axis of symmetry x = -2 Vertex is a minimum point Minimum y value y = -11 43) f(x) = -x2 + 6x + 4 y (3,13) 14 x f(x) 5 9 4 12 3 13 2 12 1 9 Vertex (3, 13) Axis of symmetry x = 3 Vertex is a maximum point Maximum y value y = 13 12 10 8 6 4 2 x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -6 45) k(x) = -3x2 + 6x – 7 x k(x) -1 -16 0 -7 1 -4 2 -7 3 -16 Vertex (1,-4) Axis of symmetry x = 1 Vertex is a maximum point Maximum y value y = -4 101 Answers to Odd Problems Section 5.3 47) x f(x) 2 1 1/3 0 -1 9 2 2/3 1 6 9 8 7 6 5 4 3 2 1 y x (1/3,2/3) -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 Vertex (1/3, 2/3) Axis of symmetry x = 1/3 Vertex is a minimum point Minimum y value y = 2/3 Section 5.4 1a) 5 seconds 3a) 2 seconds 5a) 1 second 7a) 14 feet 9a) 15 feet 11a) July Section 5.5 1) x=4 x = 1 is extraneous 17) 𝑥 = 0, 1/5 1 25) 𝑦 = − 27 , 1 1b) 200 feet 3b) 78.4 meters 5b) 16 feet 7b) September 9b) October 11b) 101 degrees 3) y=9 y = 25 is extraneous 11) x = -9, -2 5) x=4 x = 16 is extraneous 13) y = -5, -3 19) x= -3/5, -1 27) x = -216, 1 21) 𝑦 = ±3𝑖, ±1 29) y = 243, 1 15) 𝑥 = 7, 22/5 23) 𝑎 = ±√6𝑖, ±1 102 Answers to Odd Problems Section 5.6 1a) x = -4,3 1b) (−∞, −4) ∪ (3, ∞) 1c) (-4,3) 1d) (−∞, −4] ∪ [3, ∞) 1e) [-4,3] 3a) x = -4,3 3b) (-4,3) 3c) (−∞, −4) ∪ (3, ∞) 3d) [-4,3] 3e) (−∞, −4] ∪ [3, ∞) 5a) x = 2 5b) (−∞, ∞) 5c) No solution 5d) (−∞, ∞) 5e) x = 2 7a) x = 3 7b) No Solution 7c) (−∞, 3) ∪ (3, ∞) 7d) x = 3 7e) (−∞, ∞) 9a) No Solution 9b) No Solution 9c) (−∞, ∞) 9d) No Solution 9e) (−∞, ∞) 11a) No Solution 11b) ( −∞, ∞) 11c) No Solution 11d) (−∞, ∞) 11e) No Solution 13a) x = -8, 2 13b) (−∞, −8) ∪ (2, ∞) 13c) (-8,2) 13d) (−∞, −8] ∪ [2, ∞) 13e) [-8,2] 15a) x =1, 5 15b) (−∞, 1) ∪ (5, ∞) 15c) (1,5) 15d) (−∞, 1] ∪ [5, ∞) 15e) [1,5] 17a) x = 1, 5 17b) (−∞, 1) ∪ (5, ∞) 17c) (1,5) 17d) (−∞, 1] ∪ [5, ∞) 17e) [1,5] 19a) x = -11, 3 19b) (-11,3) 19c) (−∞, −11) ∪ (3, ∞) 19e) (−∞, −11] ∪ [3, ∞) 19e) [-11,3] 21a) x = 0, 10 21b) (0,10) 21c) (−∞, 0) ∪ (10, ∞) 21d) [0,10] 21e) (−∞, 0] ∪ [10, ∞) 23a) x = -6 23b) No solution 23c) (−∞ − 6) ∪ (−6, ∞) 23d) x = -6 23e) (−∞, ∞) it would also be correct to write (−∞, −6] ∪ [−6, ∞) although the first answer is preferable. 25a) No Solution 25b) (−∞, ∞) 25c) No solution 25d) (−∞, ∞) 25e) No solution 27a) No Solution 27b) (−∞, ∞) 27c) No solution 27d) (−∞, ∞) 27e) No solution 103