Originally Posted by

**Winding Function** Shouldn't a*x^2 + b*x + c be in absolute value code?

Ok, same dif:

Code:

In[11]:=
Maximize[{Abs[a] + Abs[b] + Abs[c],
{Abs[a*x^2 + b*x + c] <= 100 &&
Abs[x] <= 1 && Element[{a, b, c},
Reals]}}, {a, b, c, x}]
During evaluation of In[11]:= Maximize::natt:
The maximum is not attained at any point satisfying the given \
constraints. >>
Out[11]=
{Infinity, {a -> Indeterminate,
b -> Indeterminate, c -> Indeterminate,
x -> Indeterminate}}

For any large value of a, I can find suitable large negative (or positive) values of b and/or c such that $\displaystyle Abs[ax^2+bx+c]\leq 100$.