Answer
See below.
Work Step by Step
Let's compare $f(x)=3x^2-6x+4$ to $f(x)=ax^2+bx+c$. We can see that a=3, b=-6, c=4. a>0, hence the graph opens up, hence its vertex is a minimum. The minimum value is at $x=-\frac{b}{2a}=-\frac{-6}{2\cdot 3}=1.$ Hence the minimum value is $f(1)=3(1)^2-6(1)+4=1.$
