true 5. 6. Let = one of the numbers; x 8 = the other number. x − 6. 8 8x x x2 − − 2 ; The product is 7. 40 ; x − −x ( ) ( 8) f x x x = − 40 x 8x + x2 = − The of the minimum is x-coordinate x b = − = − Exercise Set 2.2 4. −8 −8 = 2a 2 (1) 1. vertex: (1, 1) 2 (4) (4)2 f = − 8 (4) ( ) 1)2 1 h x ( x 16 32 = − = −16 (4, The vertex is . −16) The minimum product is . This occurs when the −16 two numbers are 4 and 4 8 . − = −4 = − + 2. vertex: (–1, 1) ( ) ( g x x = +1)2 +1
5. true 6. Let x = one of the numbers; x − 8 = the other number. 6. x − 8 ; x2 − 8x 2 The product is f ( x ) = x ( x − 8) = x2 − 8x 7. 40 − x ; −x + 40 x The x-coordinate of the minimum is x = − b = − −8 −8 = 4. Exercise Set 2.2 2a 2 (1) 2 1. vertex: (1, 1) f (4) = (4)2 − 8 (4) h ( x ) ( x 1)2 1 = 16 − 32 = −16 The vertex is (4, −16) . The minimum product is −16 . This occurs when the two numbers are 4 and 4 − 8 = −4 . = − + 2. vertex: (–1, 1) g ( x ) = ( x +1)2 +1