Explanation Given Information: The trajectory of a ball hit by a baseball player is provided by a quadratic expression y = − 0.002975 x 2 + 1.3875 x + 3.75 where y represents the height of the ball along the ground and x represents the position of ball along the ground from the home plate, both measured in feet. Formula used: For a quadratic equation of the form a x 2 + b x + c , the x coordinate of the vertex can be found using the formula, x = − b 2 a A parabola is known to be symmetric about its vertex. Hence, for a parabola of the form y = a x 2 + b x + c , is known to be symmetric about its vertex. Calculation: Consider the equation of the parabola provided in the question, y = − 0.002975 x 2 + 1.3875 x + 3.75 Now, the vertex of the above parabola trajectory of the ball will be the highest point of the ball. The x -coordinate of the point can be evaluated by the formula, x = − b 2 a Compare the provided equation y = − 0.002975 x 2 + 1.3875 x + 3.75 with y = a x 2 + b x + c , substitute 1

Pathways to Math Literacy with 18 Week ALEKS Access Card

1st Edition

ISBN: 9781259278723

Author: David Sobecki Professor, Brian A. Mercer

Publisher: McGraw-Hill Education

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 4.9, Problem 9C

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To calculate: The maximum horizontal distance achieved by a ball whose trajectory is provided by a quadratic expression y=−0.002975x2+1.3875x+3.75 where y represents the height of the ball along the ground and x represents the position of ball along the ground from the home plate.

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Chapter 4.9, Problem 8C

Chapter 4.9, Problem 10C

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Pathways to Math Literacy with 18 Week ALEKS Access Card

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The maximum horizontal distance achieved by a ball whose trajectory is provided by a quadratic expression y = − 0.002975 x 2 + 1.3875 x + 3.75 where y represents the height of the ball along the ground and x represents the position of ball along the ground from the home plate.

Solution Summary: The author calculates the maximum horizontal distance achieved by a ball whose trajectory is provided by the quadratic expression y=-0.002975x2+1.3875x+3.75.

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To calculate: The maximum horizontal distance achieved by a ball whose trajectory is provided by a quadratic expression y=−0.002975x2+1.3875x+3.75 where y represents the height of the ball along the ground and x represents the position of ball along the ground from the home plate.

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Chapter 4 Solutions