Final answer:
An object's potential energy is affected by its mass and vertical position within a gravitational field, not by its velocity or horizontal position.
Step-by-step explanation:
The factors that affect an object's potential energy include its mass (A) and its vertical position (B) within a gravitational field. Whereas velocity (C) is associated with an object's kinetic energy, and horizontal position (D) does not directly affect its potential energy when there is no change in height relative to a reference point.
Essentially, potential energy can be seen as energy that is stored and has the capacity to do work in the future. For example, a ball placed at the top of a hill has gravitational potential energy due to its elevated position and mass. As the ball rolls down, its potential energy decreases while its kinetic energy increases, maintaining conservation of mechanical energy.