3 3 = −2 + 6 + 2 ( = x) x2 x f x) 32. ( ) = −2 − 3x + 2 x2 34. 2 + 4 ( x2 f − 1 x = + − 2 2 1 x2 x = −2 ⎛ − + ⎞ + 3x 9 2 x2 ( ) + 9 3 ⎜ ⎟ 4 2 ⎝ ⎠ 2 2 3 −1 − 3 = −2 ⎛ x − = 3 + 2 x + ( 13 + 1) x ⎝ 2 ⎠ 2 ( = 2 + 1)2 − 5 x Using the graph of = , right 3 units, 3 3 y x2 2 reflect about the stretch vertically by a Using the graph of = x-axis, , shift left 1 unit, y x2 2 , then shift factor of 2, then shift up 13 units. compress vertically by a factor of 3 2 down 5 3 unit. 33. ( = 1 + −1 f x) x2 x = + = = = 35. a. For ( 2x , 1 , 2 , 0. f x) x2 a b c 2 ( ) = 1 + 2 x2 x Since = 1 > 0 , the graph opens a − 1 up. The of the vertex is x-coordinate ( = 1 + 2 + 1) x2 x −b −(2) −2 −1 − 1 2 2 . = = = = −1 x 2a 2(1) 2 2 2 ( = + 1 1)2 x The of the vertex is y-coordinate − 3 + = − = −1. (−1)2 2(−1) 1 2 Using the graph of ⎝ ⎠ ⎛ −b ⎞ = = (−1) f f = , left 1 unit, y x2 compress vertically by a factor of 1 , then shift down 3 units. 2 2
32. f ( x) = −2 x2 + 6 x + 2 = −2 ( x2 − 3x ) + 2 34. f ( x) = 2 x2 + 4 3 3 x − 1 = 2 x2 + 2 x − 1 = −2 ⎛ x2 − 3x + 9 ⎞ + 2 + 9 3 ( ) ⎜ 4 ⎟ 2 ⎝ ⎠ 2 2 = −2 ⎛ x − 3 + 13 = 3 ( x + 2 x + 1) −1 − 3 ⎝ 2 ⎠ 2 = 2 ( x + 1)2 − 5 Using the graph of y = x2 , right 3 units, 3 3 2 reflect about the x-axis, stretch vertically by a Using the graph of y = x2 , shift left 1 unit, 2 factor of 2, then shift up 13 units. 2 compress vertically by a factor of , then shift 3 down 5 3 unit. 33. f ( x) = 1 x2 + x −1 2 35. a. For f ( x) = x2 + 2x , a = 1 , b = 2 , c = 0. = 1 ( x2 + 2 x ) − 1 Since a = 1 > 0 , the graph opens up. The x-coordinate of the vertex is = 1 ( x2 + 2 x + 1) −1 − 1 −b −(2) −2 2 2 x = = = = −1 . 2a 2(1) 2 = 1 ( x + 1)2 − 3 2 2 The y-coordinate of the vertex is Using the graph of y = x2 , left 1 unit, f ⎛ −b ⎞ = f (−1) = (−1)2 + 2(−1) = 1 − 2 = −1. ⎝ ⎠ compress vertically by a factor of 1 , then shift 2 down 3 units. 2
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