a. = 2. The parabola opens upward and has a The axis of symmetry is = 1. x minimum value. 40. = 2x2 8x 3 f(x) – – b. 8 2 x = −b = = 2a 4 = 2(2)2 8(2) 3 f(2) – – = 8 16 3 = – – –11 The minimum is at 2 . x –11 = ( 8x 3 f x) x2 = −4 + − domain: (−∞, ∞) c. domain: (−∞, ∞) 41. (−∞, range: −1] [−11, range: ∞) ( 6 4 f x) x = − + a. = -4. The parabola opens downward and a 38. has a maximum value. x2 ( 4x f x) x2 = − + 6 b. 1 x = −b = −8 = 2a −8 (x2 ( 4 4)+ f x) x = − + (1) 8(1) 3 f = −4(1)2 + − 8 3 = −4 + − = 6 4 − 1 ( ( 2)2 2 f x) x The maximum is 1 at 1 . = − + x = vertex: (2, 2) x-intercepts: domain: (−∞, c. ∞) (−∞,1] range: ( 0 2)2 x = − 42. = 12x + 3 2 f(x) –2x2 – + ( 2)2 x − = a. = The parabola opens downward a –2. and has a maximum value. −2 2 x − = ±i 12 2 −b 2 x i = ± b. x = = = −3 2a 2 −4 The axis of symmetry is = 2. x No x-intercepts y-intercept: = 12(–3) + 3 f(–3) –2(–3)2 – (0) (0)2 (0) 6 4 f = − + = + 36 + 3 = 21 –18 The maximum is 21 at . 6 x = −3 = c. domain: (−∞, ∞) (−∞, range: 21] a. = 5. The parabola opens upward and has a a 43. minimum value. ( 5x2 5x f x) = −
The axis of symmetry is x = 1. 40. f(x) = 2x2 – 8x – 3 a. a = 2. The parabola opens upward and has minimum value. b. x = −b = 8 = 2 2a 4 f(2) = 2(2)2 – 8(2) – 3 = 8 – 16 – 3 = –11 The minimum is –11 at x = 2 . domain: (−∞, ∞) range: (−∞, −1] 41. c. domain: (−∞, ∞) f ( x) = −4 x2 + 8x − 3 range: [−11, ∞) 38. f ( x) = 6 − 4 x + x2 a. a = -4. The parabola opens downward and has a maximum value. f ( x) = x2 − 4x + 6 b. x = −b = −8 = 1 2a −8 f ( x) = (x2 − 4 x + 4)+ 6 − 4 f ( x) = ( x − 2)2 + 2 f (1) = −4(1)2 + 8(1) − 3 = −4 + 8 − 3 = 1 The maximum is 1 at x = 1 . vertex: (2, 2) x-intercepts: 0 = ( x − 2)2 + 2 c. domain: (−∞, ∞) 42. f(x) = –2x2 – 12x + 3 range: (−∞,1] ( x − 2)2 = −2 a. a = –2. The parabola opens downward and has a maximum value. x − 2 = ±i 2 −b 12 x = 2 ± i 2 b. x = = = −3 2a −4 No x-intercepts y-intercept: f (0) = 6 − 4 (0) + (0)2 = 6 The axis of symmetry is x = 2. f(–3) = –2(–3)2 – 12(–3) + 3 = –18 + 36 + 3 = 21 The maximum is 21 at x = −3 . c. domain: (−∞, ∞) range: (−∞, 21] 43. f ( x) = 5x2 − 5x a. a = 5. The parabola opens upward and has a minimum value.
Precalculus-Essentials-5th-Edition-Blitzer-Solutions-Manual.docx