Answer
The given equation is symmetric about the origin.
Work Step by Step
$y=x^{3}+10x$
Test for symmetry about the $y$-axis by substituting $x$ by $-x$ and simplifying:
$y=(-x)^{3}+10(-x)$
$y=-x^{3}-10x$
Since substituting $x$ by $-x$ does not yield an equivalent equation, the equation is not symmetric about the $y$-axis.
Test for symmetry about the $x$-axis by substituting $y$ by $-y$ and simplifying:
$-y=x^{3}+10x$
Since substituting $y$ by $-y$ does not yield an equivalent equation, the equation is not symmetric about the $x$-axis.
Test for symmetry about the origin by substituting $x$ by $-x$ and $y$ by $-y$ and simplifying:
$-y=(-x)^{3}+10(-x)$
$-y=-x^{3}-10x$
$y=x^{3}+10x$
Since substituting $x$ by $-x$ and $y$ by $-y$ yields an equivalent equation, the equation is symmetric about the origin.