Explanation Given Information: The trajectory of a ball hit by a baseball player is provided by a quadratic expression y = − 0.003 x 2 + 1.046 x + 3.1 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 = − 0.003 x 2 + 1.046 x + 3.1 Now, the vertex of the 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 = − 0.003 x 2 + 1.046 x + 3.1 with a x 2 + b x + c = y , substitute 1

1st Edition

ISBN: 9781259218859

Author: David Sobecki Professor, Brian A. Mercer

Publisher: McGraw-Hill Education

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Chapter 4.9, Problem 10A

To determine

To calculate: The distance from the home plate where the ball land whose trajectory is provided by a quadratic expression y=−0.003x2+1.046x+3.1 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 9A

Chapter 4.9, Problem 11A

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The distance from the home plate where the ball land whose trajectory is provided by a quadratic expression y = − 0.003 x 2 + 1.046 x + 3.1 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 distance from the home plate where the ball land whose trajectory is provided by a quadratic expression.

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To calculate: The distance from the home plate where the ball land whose trajectory is provided by a quadratic expression y=−0.003x2+1.046x+3.1 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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