1. The maximum value $M(a)$ of the function $f(x)=\left|x^{2}-a\right|$ in the interval $[-1,1]$ has its minimum value as $\qquad$ .
$$
\text { 2.1. } \frac{1}{2} \text {. }
$$
(1) When $a \leqslant 0$, it is easy to see that $M(a)=1-a$.
(2) When $a>0$, $M(a)=\max \{a,|1-a|\}$.

When $0<a \leq \frac{1}{2}$, $M(a)=1-a$; when $a>\frac{1}{2}$, $M(a)=a$.
Therefore, $(M(a))_{\min }=\frac{1}{2}$.