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 $0$.