**Y-axis symmetry: **

The graph of an equation is symmetric with respect to the y-axis if an equivalent equation is obtained when x is replaced by -x.

ex.

x^{2} = 2y

(-x)^{2 }= 2y = x^{2 }= 2y

this equation is symmetric about the y-axis.

**X-axis symmetry:**

The graph of an equation is symmetric with respect to the x-axis if an equivalent equation is obtained when y is replaced by -y.

ex.

y^{6}= 4x

(-y)^{6 }= 4x = y^{6} = 4x

this equation is symmetric about the x-axis.

**Origin Symmetry:**

The graph of an equation is symmetric with respect to the origin if an equivalent equation is obtained when x is replaced by -x and y replaced by -y.

ex.

x^{3 }= y

(-x)^{3} = -y

-x^{3} = -y = x^{3} = y

this equation is symmetric about the origin.