Final answer:
The trajectory of a particle can be described by the parametric equation y = ax + bx², which represents a parabolic path. This equation can be derived by solving the equations of motion for a projectile that starts at the origin.
Step-by-step explanation:
The trajectory of a particle can be described by the parametric equation y = ax + bx², which represents a parabolic path. This equation can be derived by solving the equations of motion for a projectile that starts at the origin. Using the expression x = V₀t and substituting it into the equation y = V₀yt - (1/2)gt², we obtain the equation y = ax + bx², where a and b are constants.