Kwadratische modellen

When a ball is thrown into the air, it follows a curved path called projectile motion—the path an object takes under the influence of gravity.

This vertical motion under constant acceleration is modelled using a quadratic function of time. The function has three terms: a t-squared term, a t term, and a constant.

The graph of this function is a downward-opening parabola. It shows the ball rising, reaching its highest point, then falling.

Completing the square rewrites the equation into the standard form of a parabola, revealing the vertex—the highest point of the motion. The time at which this occurs is given by negative b over 2a.

Each term of the quadratic equation represents a physical quantity that affects the ball’s height.

The t-squared term reflects the constant acceleration due to gravity, which curves the path downward.

The coefficient of the linear t represents the initial velocity, which determines how quickly the ball rises.

The constant term represents the initial height from which the ball is thrown.

Using the updated coefficients, substituting the time value into the function gives the highest point of the ball's flight.