刟1. When $0 \leqslant x \leqslant 1$, find the maximum and minimum values of the quadratic function $y=x^{2}-2 a x+4$.

When $0 \leqslant x \leqslant 1$, find the maximum and minimum values of the quadratic function $y=x^{2}-2 a x+4$.
Let $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-2 \mathrm{ax}+4$ have a maximum value of $\mathrm{M}$ and a minimum value of $\mathrm{m}$.
$$
\begin{aligned}
f(x) & =x^{2}-2 a x+4 \\
& =(x-a)^{2}+\left(4-a^{2}\right) .
\end{aligned}
$$

First, find the maximum value $M$.
(i) When $a>1$ (i.e., the axis of symmetry passes through the right side of the domain), $m=f(1) = 5-2a$.
$$
\text{In summary, } m=\left\{\begin{array}{ll}
4, & \text{when } a \leq 1; \\
5-2a, & \text{when } a > 1.
\end{array}\right.
$$