f(x) = 3x^2 + 6x - 8
The x coordinate of the vertex = -6 / [ 2 * 3] = -6/6 = -1
This is a parabola that turns upward......the vertex is the minimum point
The y coordinate of the vertex = 3(-1)^2 + 6(-1) - 8 = 3 - 6 - 8 = -11
So.....the range is [ -11, infinity )