Final answer:
The equation y = ax^2 + bx represents a parabola, which describes the trajectory of a projectile in motion. Proving this requires substitution of the horizontal motion equation into the vertical motion equation, and the acceleration versus time graph for a projectile is a constant negative value.
Step-by-step explanation:
The trajectory equation y = ax^2 + bx is a simplified form representing the path of a projectile in a parabolic motion. The projectile trajectory can be derived using the kinematic equations for horizontal and vertical motion. Proving the trajectory follows a parabola requires solving for time (t) from the horizontal motion equation (x = Voxt), and substituting it into the vertical motion equation (y = Voyt - (1/2)gt2), which results in an equation of a parabola with constants a and b, that correspond to initial velocity components and the acceleration due to gravity. To understand the trajectory of a projectile, it is essential to analyze the physics involved in projectile motion.
When analyzing the vertical acceleration versus time graph for a projectile with a constant horizontal velocity and affected by gravity, the graph is a horizontal line representing a constant negative acceleration due to gravity, as there are no other forces acting on it in the vertical direction after the initial launch.