2. Let $f(x)$ be a quadratic function, and $2 x^{2}-4 x+3 \leqslant f(x) \leqslant 3 x^{2}-6 x+4, f(3)=11$, then $f(5)=$
Solve:
$$
2(x-1)^{2}+1 \leqslant f(x) \leqslant 3(x-1)^{2}+1 \Rightarrow f(x)=k(x-1)^{2}+1 \text {, }
$$

Substitute $f(3)=4 k+1=11 \Rightarrow k=\frac{5}{2}$. Therefore, $f(5)=\frac{5}{2} \times 16+1=41$.