**Example QF.1.1 **:$q(x) = x^2$. " Square x" : $x^2$ **The core quadratic
function.**

The arrows in the mapping diagram all end at a point with value $\ge
0$.

The arrows for $a$ and $-a$ hit the same value $q(a) = a^2$ on the
target axis.

The smallest value of $q$ is $q(0)=0$

**Motion Interpretation:** If $x$ is time and $q(x)$ is the
position of an object on the target axis at time $x$, then the
object is moving down before time $0$ and up after time $0$. At time
$0$ the object is at its lowest point at level $0$.