A quadratic function is a mathematical function that can be used to graph a parabola, which is an arc with a vertical plane of symmetry. A projectile that is propelled from the Earth and then drawn back by gravity follows a parabolic curve. A baseball often follows this trajectory, which makes quadratic functions highly applicable to the game of baseball.
Hitting
When you hit a baseball, you transfer your weight when swinging to exert a force on the ball with your bat. This force sends the ball flying forward and upward. As the ball is traveling upward, the downward force of gravity causes the ball to decelerate. The ball eventually stops moving upward at the maximum height of its trajectory, and accelerates downward because of gravitational force. The path taken by the baseball in this situation can be described using a quadratic function because the ball is launched upward by the bat and then pulled downward by gravity, following a parabolic curve.
Throwing
When you hurl a baseball from the outfield to home plate, you might notice that the baseball follows a trajectory that resembles a parabola. When you throw the baseball, you exert a forward and upward force on the ball toward a target player, much like when you hit the ball with a bat. Once again, gravity causes the ball to decelerate and eventually accelerate downward, creating a parabolic path that can be described using a quadratic function.
Grounders
If you have ever seen a ground ball bouncing, you'll notice that each bounce follows a parabolic path. When the ball first hits the ground, the ground exerts a normal force on the ball that propels it upward, much like when the ball is hit with a bat. As the ball bounces upward, gravitational force once again causes the ball to decelerate upward and eventually fall downward. The trajectory of this arc can be described using the quadratic equation because it is parabolic. Each time the ball bounces, energy is lost due to friction between the ball and the ground. This means that each successive bounce is lower than the previous one, until the ball eventually rolls on the ground and comes to a complete stop.
Considerations
Though a quadratic function can be used to estimate a baseball's trajectory, it often does not perfectly describe a baseball's motion. This is because many factors, including wind, altitude, temperature and humidity impact the ball's trajectory, and must considered when mathematically determining a baseball's path, according to the website The Class Zone.
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