Given the quadratic function f(x) = x²-6x+13, notice that we can write it like this:
[tex]\begin{gathered} f(x)=x²-6x+13=x²-6x+9+4=(x-3)²+4 \\ \Rightarrow f(x)=(x-3)²+4 \end{gathered}[/tex]
thus, the vertex form of f(x) is (x-3)²+4.
The minimum value of f will be on the vertex of the function. Therefore, the minimum value of f(x) is 4
