Explanation Procedure used: “ Procedure for finding intercepts: 1. To find the x - intercept, if any, of the graph of an equation, let y = 0 in the equation and solve for x . 2. To find the y - intercept, if any, of the graph of an equation, let x = 0 in the equation and solve for y ”. Rules used: “ Test for Symmetry: To test the graph of an equation for symmetry with respect: x - Axis : Replace y by – y in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the x -axis. y - Axis : Replace x by– x in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the y -axis. Origin : Replace x by– x and y by – y in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the origin”. Calculation: Obtain the x -intercept point of the given equation as follows. Set y = 0 and solve the equation for x as, x 4 − 2 x 2 − 8 = 0 x 4 − 4 x 2 + 2 x 2 − 8 = 0 x 2 ( x 2 − 4 ) + 2 ( x 2 − 4 ) = 0 ( x 2 − 4 ) ( x 2 + 2 ) = 0 Simplify further, ( x 2 − 4 ) = 0 or ( x 2 + 2 ) = 0 x 2 = 4 or x 2 = − 2 x = ± 2 or x = ± 2 i Here, x -intercepts are considered only on real number system. Thus, the possible x -intercepts are x = ± 2 . Thus, the x -intercept point of the given equation is ( − 2 , 0 ) and ( 2 , 0 ) . Obtain the y -intercept point of the given equation as follows. Set x = 0 and solve the equation for y as, y = ( 0 ) 4 − 2 ( 0 ) 2 − 8 = 0 − 0 − 8 = − 8 Thus, the y -intercept points of the given equation is ( 0 , − 8 ) . Therefore, the intercepts points of the equation y = x 4 − 2 x 2 − 8 are ( 0 , − 8 ) , ( − 2 , 0 ) and ( 2 , 0 )

College Algebra: Concepts Through Functions (4th Edition)

4th Edition

ISBN: 9780134686967

Author: Michael Sullivan, Michael Sullivan III

Publisher: PEARSON

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Chapter F.2, Problem 60AYU

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The intercepts points of the equation y=x4−2x2−8 and test for symmetry.

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Chapter F.2, Problem 59AYU

Chapter F.2, Problem 61AYU

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Chapter F Solutions

College Algebra: Concepts Through Functions (4th Edition)

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