Example QF.1.4 : $ q(x) = 2x^2$. "
Constant multiple": $2$
The arrows in the mapping diagram all end at a point with value $\ge
The arrows for $x=a$ and $x=-a$ hit the same value $q(x) = 2 a ^2$
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 $0$.