Example QF.1.2 :$q(x) = x^2 +2$. " Added value after  $x^2$": 2.
The arrows in the mapping diagram all end at a point with value $\ge 2$.
The arrows for $a$ and $-a$ hit the same value $q(a) = a^2 +2$ on the target axis.
The smallest value of $q$ is $q(0)=2$
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 $2$.