Question

Symmetry. Test the equation for symmetry

$y=x^2+\left|x\right|$

Short answer

The equation is symmetry about the y-axis

Step-by-step solution

Step 1. concept of symmetry.

Symmetry with respect to thex-axis can be identified by replacing $y\mathrm{by}-y$. The resulting equation is equivalent to the original one.

Symmetry with respect to the y-axis can be identified by replacing $x\mathrm{by}-x$. The resulting equation is equivalent to the original one.

Symmetry with respect to the origin can be identified by replacing $x\mathrm{by}-x$ and $y\mathrm{by}-y$. The resulting equation is equivalent to the original one.

Step 2. Given equation. 

$y=x^2+\left|x\right|$

Step 3. Determining the symmetry.

If x is replaced by $-x$and in the equation $y=x^2+\left|x\right|$

$y={(-x)}^2+|-x|$(Replace x by $-x$)

$y=x^2+\left|x\right|$ (Simplify)

and so the equation is equivalent to the original one.

$\therefore$ the graph is symmetry about the y-axis