Explanation:
y = 2x^2 - 4x -3 a = 2 b=-4 c = -3
This is a bowl shaped parabola
Minimum value will occur at x = - b/2a = 4/4 = 1
calculate this minimum value at x = 1 to be y = -5
the two arms of the parabola go up to + inf from there
range = [-5, +∞)