Question 26: If the graph of the function $f(x)=(x+a)(|x-a|+|x-2022|)$ is centrally symmetric, then the value of the real number $a$ is $\qquad$
Question 26, Solution: Let $m=\min \{a, 2022\}, M=\max \{a, 2022\}$. Then
$$
f(x)=\left\{\begin{array}{c}
-2 x^{2}+(2022-a) x+a(2022+a), \text { when } x \in(-\infty, m) \\
(M-m)(x+a), \text { when } x \in[m, M] \\
2 x^{2}-(2022-a) x-a(2022+a), \text { when } x \in(M,-\infty)
\end{array}\right.
$$

Notice that the x-coordinates of the vertices of the two parabolas corresponding to $x \in(-\infty, m)$ and $x \in(M,-\infty)$ are both $\frac{2022-a}{4}$, and the x-coordinate of the midpoint of the line segment corresponding to $x \in[m, M]$ is $\frac{m+M}{2}=\frac{2022+a}{2}$. Therefore, it must be that $\frac{2022-a}{4}=\frac{2022+a}{2}$, solving which gives $a=-674$. Upon verification, this satisfies the conditions.