smc

The $x$ value at which the minimum value of this quadratic (of the form $a{x}^2+bx+c$) occurs is $\frac{-b}{2a}=-\frac{-6}{2\cdot 1}=3$. The minimum value of the quadratic is therefore at $$3^2-6\cdot 3+13$$ $$=9-18+13$$ $$=4.$$ So, the answer is $\boxed{4}$.