Answer
$-22$
Work Step by Step
As we are given that $f(x)=3x^2-18x+5$
Here, $a=3,b=-18,c=5$
and $a =3 \gt 1$ and this shows a minimum value at the point $h=\dfrac{-b}{2a}=-\dfrac{(-18)}{2(3)}=3$
Now, $f(3)=3(3)^2-18(3)+5$
Thus, the minimum value of the function is: $f(3)= -22$