document.write( "Question 785270: Determine whether the graph of y= 3+ x^2 is symmetric with respect to the x- axis, the y-axis or the origin. \n" ); document.write( "

Algebra.Com's Answer #477489 by KMST(5328) $\"\"$ $\"About$

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In the graph of $\"y=3%2Bx%5E2\"$ all the points are above the x-axis $\"y%3E=3%3E0\"$ , so it could not be symmetric with respect to the x- axis, or the origin.
\n" ); document.write( "Since $\"y=3%2Bx%5E2=3%2B%28-x%29%5E2\"$ , for each point (x,y) in the graph there is a corresponding (-x,y) point at the same distance to the other side of the y-axis, so it is symmetric with respect to the y-axis.
\n" ); document.write( "To be symmetric with respect to the y- axis, changing $\"x\"$ to $\"-x\"$ should yield an equivalent equation, and that is true for $\"y=3%2Bx%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "To be symmetric with respect to the x- axis, changing $\"y\"$ to $\"-y\"$ should yield an equivalent equation.
\n" ); document.write( "In this case, if $\"y=3%2Bx%5E2\"$ is true, $\"-y=3%2Bx%5E2\"$ is definitely not true.\r
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\n" ); document.write( "\n" ); document.write( "To be symmetric with respect to the origin, replacing $\"-y\"$ for $\"y\"$ AND $\"-x\"$ for $\"x\"$ AT THE SAME TIME should yield an equivalent equation.
\n" ); document.write( "In this case, if $\"y=3%2Bx%5E2\"$ is true, $\"-y=3%2B%28-x%29%5E2\"$ <--> $\"-y=3%2Bx%5E2\"$ is definitely not true. \n" ); document.write( "

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