= −2 − 2 x2 26. 29. − ( = 2 4 + 1 f x) x2 x Using the graph of ( ) ( = f x) , stretch vertically by a y x2 = 2 − 2x + 1 x2 factor of 2, reflect across the then shift x-axis, down 2 units. = 2( 2 + 1) + 1 − 2 x = − −1 2( 1)2 x Using the graph of = , shift right 1 unit, y x2 stretch vertically by a factor of 2, then shift down 1 unit. = + 4 + 2 x2 x 27. = + + + − ( 4x 4) 2 4 x2 ( f x) = + − ( 2)2 2 x + 6 x Using the graph of ( ) = , shift left 2 units, then y x2 ( f shift down 2 units. = + 3 2 x2 x x) = 3( + 2 + 1) − 3 = x2 x 30. = 3( + 1)2 − 3 x Using the graph of = , shift left 1 unit, y x2 stretch vertically by a factor of 3, then shift down 3 units. = − 6 − 1 x2 x 28. = ( − 6 + 9) −1 − 9 x2 x ( f x) = ( − 3)2 − 10 x Using the graph of = , shift right 3 units, y x2 then down 10 units. ( ) 31. = − + 2x x2 = −( + 2 + 1) + 1 x2 x = − − ( 2 f x) x2 x = −( + 1)2 + 1 x Using the graph of = , shift left 1 unit, y x2 reflect across the then shift up 1 unit. x-axis,
26. f ( x) = −2 x2 − 2 Using the graph of y = x2 , stretch vertically by a 29. f ( x) = 2 x2 − 4 x + 1 = 2 ( x2 − 2x ) + 1 factor of 2, reflect across the x-axis, then shift down 2 units. = 2( 2 x + 1) + 1 − 2 = 2( x − 1)2 −1 Using the graph of y = x2 , shift right 1 unit, stretch vertically by a factor of 2, then shift down 1 unit. 27. f ( x) = x2 + 4 x + 2 = ( x2 + 4x + 4) + 2 − 4 = ( x + 2)2 − 2 Using the graph of shift down 2 units. y = x2 , shift left 2 units, then 30. f ( x) = + 6 x = 3 ( x2 + 2 x ) = 3( x2 + 2 x + 1) − 3 = 3( x + 1)2 − 3 Using the graph of y = x2 , shift left 1 unit, stretch vertically by a factor of 3, then shift down 3 units. 28. f ( x) = x2 − 6 x − 1 = ( x2 − 6 x + 9) −1 − 9 = ( x − 3)2 − 10 Using the graph of y = x2 , shift right 3 units, then down 10 units. 31. f ( x) = − x2 − 2 x = − ( x2 + 2x ) = −( x2 + 2 x + 1) + 1 = −( x + 1)2 + 1 Using the graph of y = x2 , shift left 1 unit, reflect across the x-axis, then shift up 1 unit.
Downloadable-Solution-Manual-for-Precalculus-Concepts-Through-1.docx