Final answer:
The given quadratic equation represents the flight of a football across a field, demonstrating a parabolic trajectory. The coefficient values determine the shape of the parabola.
Step-by-step explanation:
The given quadratic equation, -1/75x^2 + 6/5x, represents the flight of a football across a field. In this equation, x represents the distance traveled and y represents the height of the ball. The equation is of the form y = ax + bx², which is the equation of a parabola. The coefficient 'a' represents the linear term and the coefficient 'b' represents the quadratic term. In this case, a = 6/5 and b = -1/75.
The parabolic shape of the trajectory is a result of the combination of vertical and horizontal motion. The ball follows a curved path due to the influence of gravity and the initial velocity. The quadratic term in the equation accounts for the vertical motion of the ball, while the linear term represents the horizontal motion. The coefficients determine how steep or wide the parabola is.