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 $0$.