Explanation Given Information: The system of provided inequalities are: y + 1 ≥ x 2 y + 1 ≤ − x 2 Graph: Consider the provided inequalities: y + 1 ≥ x 2 y + 1 ≤ − x 2 Consider first inequality: y + 1 ≥ x 2 Consider the provided inequality as an equation to construct the graph. y + 1 = x 2 Above equation can be written as y = x 2 − 1 Substitute x = − 1 in y = x 2 − 1 : y = ( − 1 ) 2 − 1 y = 1 − 1 y = 0 Substitute x = 0 in y = x 2 − 1 : y = ( 0 ) 2 − 1 y = 0 − 1 y = − 1 Substitute x = 1 in y = x 2 − 1 : y = ( 1 ) 2 − 1 y = 1 − 1 y = 0 Table of above observations for y = x 2 − 1 : x − value y − value − 1 0 0 − 1 1 0 graph of above table for y = x 2 − 1 : This curve divides the graph into two regions, so test one random point from each region: The Inside region: Take a point ( 0 , 0 ) and test this value for the provided first inequality: y + 1 ≥ x 2 Substitute 0 for x and 0 for y and simplify: 0 + 1 ≥ 0 1 ≥ 0 The inequality holds true. Therefore, the inside region contains the solution to the inequality. Shade that region. The Outside region: Take a point ( 3 , 0 ) and test this value for the provided first inequality: y + 1 ≥ x 2 Substitute 3 for x and 0 for y and simplify: 0 + 1 ≥ ( 3 ) 2 1 ≥ 9 The inequality holds false. Therefore, the outside region does not contain the solution to the inequality. The obtained shaded graph is: Consider the second provided inequality: y + 1 ≤ − x 2 Consider the provided inequality as an equation to construct the graph

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ISBN: 9780073384511

Author: Julie Miller, Molly O'Neill, Nancy Hyde

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 13.5, Problem 54PE

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To graph: The compound inequalities y+1≥x2 and y+1≤−x2.

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Chapter 13.5, Problem 53PE

Chapter 13.5, Problem 55PE

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Chapter 13 Solutions

Beginning and Intermediate Algebra

Ch. 13.1 - Find the distance between the points ( − 4 , − 2 )...Ch. 13.1 - Prob. 2SP Ch. 13.1 - Prob. 3SP Ch. 13.1 - Prob. 4SP Ch. 13.1 - Prob. 5SP Ch. 13.1 - Prob. 6SP Ch. 13.1 - Prob. 7SP Ch. 13.1 - Prob. 8SP Ch. 13.1 - Prob. 1PE Ch. 13.1 - Prob. 2PE

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To graph: The compound inequalities y + 1 ≥ x 2 and y + 1 ≤ − x 2 .

Solution Summary: The author analyzes the compound inequalities y+1ge x2 and

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To graph: The compound inequalities y+1≥x2 and y+1≤−x2.

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Chapter 13 Solutions