9. The minimum value of the function $y=\sqrt{x^{2}+1}+\sqrt{x^{2}-4 x+8}$ is
9. $\sqrt{13}$ Hint: $y=\sqrt{(x-0)^{2}+(0-1)^{2}}+\sqrt{(x-2)^{2}+(0-2)^{2}}$, the problem is transformed into finding a point $P(x, 0)$ on the $x$-axis, such that $|P A|+|P B|$ is minimized. The symmetric point of $A$ with respect to the $x$-axis is $A^{\prime}(0,-1),\left|A^{\prime} B\right|=\sqrt{13}$, which is the required minimum value.