The graph of this function is a parabola that opens up. a=3, b=6 and c= -8.
The vertex is at x = -b / (2a), which here is x = -6 / (2*3) = -1. The associated y-value is f(-1) = 3(-1)^2 + 6(-1) - 8 = 3 - 6 - 8, or -11. -11 is the smallest y-value. Thus, the range of this function is [-11, infinity).