Explanation Given: A softball is thrown upward into the air at a speed of 32 feet per second from a 40-foot platform. The height of the ball after t seconds is given by the function, d ( t ) = − 16 t 2 + 32 t + 40 . Formula used: For graphing the quadratic equation , f ( x ) = a x 2 + b x + c , a ≠ 0 : The coordinates of the vertex are ( − b 2 a , f ( − b 2 a ) ) . And, The quadratic formula: a x 2 + b x + c = 0 x = − b ± b 2 − 4 a c 2 a Calculation: The initial speed of the softball is 32 feet per second. The maximum height occurs at the vertex of the parabola, d ( t ) = − 16 t 2 + 32 t + 40 . Since a = − 16 , b = 32 , and c = 40 . So, the vertex occurs at x = − b 2 a . Then, x = − 32 2 ( − 16 ) = 1 To find the y -coordinate, calculate d ( 1 )

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Chapter 8.5, Problem 37E

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To calculate: The maximum height of the softball and the time which is taken by softball to reach the ground.

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Chapter 8.5, Problem 36E

Chapter 8.5, Problem 38E

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The maximum height of the softball and the time which is taken by softball to reach the ground.

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