(8) Does there exist a quadratic function $f(x)$ such that the conditions (1) when $|x| \leqslant 1$, $|f(x)| \leqslant 1$; 
(2) $|f(2)| \geqslant 7$ are simultaneously satisfied? If it exists, find all such $f(x)$; if not, explain the reason.
(8) Exist

and only exist $f(x)=2 x^{2}-1$ and $f(x)=-2 x^{2}+1$