− + + ≤ 6 x2 x 0, = 5 t 0 t The ball strikes the ground after 5 seconds. = t b. Find the values of for which ⎝ 2 2 ⎠ 2 − − 6 ≥ x2 x 2 − 80t 0 > 96 16t ( ( − 3) + 2) x x ≥ −16t + − > 0 80t 96 0 16(t − 5t + 6) < 2 The zeros are = and = 3 . x x –2 0 ( ) 16(t − 2)(t − 3) < = − − 6 p x x2 x 0 = = 16t − 80t The zeros are 2 and 3 . t t 2 + 96 < 0 ) = 16t − 80t + s(t 2 96
− x2 + x + 6 ≤ 0 ⎝ 2 2 ⎠ t = 0, t = 5 The ball strikes the ground after 5 seconds. b. Find the values of t for which 2 x2 − x − 6 ≥ 0 80t − 16t 2 > 96 ( x − 3) ( x + 2) ≥ 0 −16t + 80t − 96 > 0 The zeros are x = –2 and x = 3 . p ( x ) = x2 − x − 6 16t 2 − 80t + 96 < 0 16(t 2 − 5t + 6) < 0 16(t − 2)(t − 3) < 0 The zeros are t = 2 and t = 3 . s(t ) = 16t 2 − 80t + 96
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