**Example QF.1.3 **:$q(x) = (x -2)^2$. "Added
value before $(...)^2$" : $x-2$

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

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

The smallest value of $q$ is $q(2)=0$

**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 $2$ and up after time $2$. At time
$2$ the object is at its lowest point at level $0$.