**Theorem: QF.COMP: For
any quadratic function,$f$, **

there are numbers **$A, h$, and $k$, so that**** $f$
can be expressed as a composition of **** the ****core ****quadratic****
function, ****$q(x) =x^2$,**** with core ****linear****
functions:**
**$f(x) = (f_{+k} \circ f_{*A} \circ q\circ
f_{-h} )(x)= A (x-h)^2 + k$**

**where $f_{+k}(u)=u+k $, $f_{-h}(u)=u-h $, **** and ****$
f_{*A}(x)=Ax$.**