When a particle falls freely under gravity from rest, its motion obeys the laws of kinematics. Specifically, displacement [d] as a function of time [t] is described by the equation d = 1/2 * g * t², where g is the acceleration due to gravity. This is a quadratic function of time, which graphs as a parabola.

In option 1, the graph is a straight line, which indicates a linear relationship between displacement and time. This doesn`t match the parabolic relationship we expect from the equation.

Option 3 shows a parabolic graph but it opens downward. This would indicate that displacement decreases over time, which is not the case for an object falling freely under gravity.

Option 4 shows a graph that is not only parabolic but also has a hump in the middle, indicating the displacement first increases then decreases with time, which again is not the scenario here.

Option 2, however, shows a parabolic graph opening upward which corresponds to the real-life scenario where displacement increases quadratically with time, as per the equation of kinematics. Hence, Option 2 is indeed the correct one.