Question 394916
I will assume the function to be {{{f(x) = 2x^2-12x-4}}}.

The domain is R, the set of all real numbers.  The graph is a parabola opening upward (a = 2 > 0) , and so the function has a minimum (corresponding to the vertex.)

{{{2x^2-12x-4 =2(x^2 - 6x) - 4 = 2(x^2 - 6x + 9) - 4 - 18  = 2(x-3)^2 - 22}}}.

The vertex is thus the point (3, -22).  So the minimum occurs at x = 3, and the minimum value is -22. 
 The range of the function is [-22, {{{infinity}}}).