document.write( "Question 643885: I accidentally put the wrong equation in my original question - I am so sorry!\r
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\n" ); document.write( "\n" ); document.write( "I am trying to test an equation for symmetry. The equation is x^2 = y^3 + 4.
\n" ); document.write( "I am starting by trying to find the intercepts. I think I found the intercepts for x - (2,0), (-2,0). I am having trouble finding the intercepts for y.
\n" ); document.write( "I substitute 0 for X and get 0 + y^3 + 4. I convert that to y^3 = -4. I am not sure where to go from there. Can I get a cube root of four? Solving for y, would my answer be the cube root of four i? Does that mean there is no y intercept?
\n" ); document.write( "I've confused myself... Thanks for any help. \n" ); document.write( "
Algebra.Com's Answer #404685 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "To test for symmetry about the x-axis,\r\n" );
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document.write( "   Substitute -y in place of y and see if it is possible to \r\n" );
document.write( "   simplify the equation back to its original form. If this\r\n" );
document.write( "   is possible it is symmetrical with respect to the x-axis.\r\n" );
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document.write( "To test for symmetry about the y-axis,\r\n" );
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document.write( "   Substitute -x in place of x and see if it is possible to \r\n" );
document.write( "   simplify the equation back to its original form. If this\r\n" );
document.write( "   is possible it is symmetrical with respect to the y-axis.\r\n" );
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document.write( "To test for symmetry about the origin,\r\n" );
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document.write( "   Substitute -x in place of x and -y in place of y and see \r\n" );
document.write( "   if it is possible to simplify the equation back to its \r\n" );
document.write( "   original form. If this is possible it is symmetrical with \r\n" );
document.write( "   respect to the x-axis.\r\n" );
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document.write( "Let's test for symmetry about the x-axis\r\n" );
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document.write( "     x² = y³ + 4\r\n" );
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document.write( "Substitute -y for y\r\n" );
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document.write( "     x² = (-y)³ + 4\r\n" );
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document.write( "     x² = -y³ + 4\r\n" );
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document.write( "That is not like the original and has one term with the opposite sign\r\n" );
document.write( "as the corresponding term in the original, so it cannot\r\n" );
document.write( "be made into the same equation as the original. \r\n" );
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document.write( "Therefore it is not symmetrical about the x axis.\r\n" );
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document.write( "Let's test for symmetry about the y-axis\r\n" );
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document.write( "     x² = y³ + 4\r\n" );
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document.write( "Substitute -x for x\r\n" );
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document.write( "  (-x)² = y³ + 4\r\n" );
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document.write( "     x² = y³ + 4\r\n" );
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document.write( "That is the same as the original so it is\r\n" );
document.write( "symmetrical with respect to the y-axis.\r\n" );
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document.write( "Let's test for symmetry about the origin\r\n" );
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document.write( "     x² = y³ + 4\r\n" );
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document.write( "Substitute -s for x and -y for y\r\n" );
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document.write( "   (-x)² = (-y)³ + 4\r\n" );
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document.write( "     x² = -y³ + 4\r\n" );
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document.write( "That is not like the original and has one term with the opposite sign\r\n" );
document.write( "as the corresponding term in the original, so it cannot\r\n" );
document.write( "be made into the same equation as the original. \r\n" );
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document.write( "Therefore it is not symmetrical about the origin.\r\n" );
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document.write( "The graph is below, but I don't think you had to do that,\r\n" );
document.write( "just test for symmetry. \r\n" );
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document.write( "Yes you can take the cube root (or any odd root) of any number.\r\n" );
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document.write( " y = ∛x²-4  \r\n" );
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document.write( "We can see it is symmetrical with respect\r\n" );
document.write( "to the y-axis, but not the x-axis or origin.\r\n" );
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document.write( "Edwin

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