Absolute value. Useful properties and graph

The absolute value $|a|$ of number $a$ may be thought of as its distance from zero. Definition of absolute value:

$$\sqrt{a^2}=|a|=\begin{cases} a, \ \ \ \text{jei} \ \ \ a \ge 0 \\ -a, \ \ \ \text{jei} \ \ \ a<0 \end{cases}$$

Useful properties: $|a|\ge 0$, $|-a|=a$, $|a-b|=|b-a|$, $|a|-|b|\le |a+b|\le |a|+|b|$