# How do you determine whether the graph of y^2=x^2 is symmetric with respect to the x axis, y axis or neither?

Jan 24, 2017

Symmetrical about both x and y axes.

#### Explanation:

For symmetry about the y axis, see if $y \left(x\right) = y \left(- x\right)$

Here you have:

$y = \pm \sqrt{{x}^{2}} = \pm \left\mid x \right\mid$.

So $y \left(- x\right) = \pm \left\mid - x \right\mid = \pm \left\mid x \right\mid$. Looks symmetrical about the y axis.

Likewise, for symmetry about the x axis, see if $x \left(y\right) = x \left(- y\right)$.

In this case:

$x = \pm \sqrt{{y}^{2}} = \pm \left\mid y \right\mid$. So $x \left(- y\right) = \pm \left\mid - y \right\mid = \pm \left\mid y \right\mid$. Looks symmetrical about the x axis.