Question 1042694
It's possible by inspection but not easy here.
First, as x becomes large negative or large positive, x^2 will be positive, so the upper range is infinite.
The minimum value for the function is not obvious.  The vertex is the lowest point, and it is at -b/2a, where b=-6 and a=3.  Therefore, the x-value for the vertex is 6/6 or 1.
When x=1, 3x^2=3
When x=1, -6x=-6
when x=1, 5=5
The minimum value is 2.  
The range is [2,oo)
{{{graph(300,300,-10,10,-10,10,3x^2-6x+5)}}}