find a real-life quadratic function
To find a real-life quadratic function, we can look at various scenarios where quadratic equations are applicable. One such scenario is the motion of objects under constant acceleration.
For example, consider an object being thrown vertically into the air. The height of the object above the ground at any given time can be modeled by a quadratic function.
Let's assume that the object is thrown with an initial velocity of 20 meters per second (m/s) and the acceleration due to gravity is approximately 9.8 m/s². We can take the ground level as the reference point for measuring height.
The equation that represents the height of the object as a function of time can be written as:
h(t) = -4.9t² + 20t
Where h(t) represents the height in meters at time t in seconds.
In this equation, the term -4.9t² represents the effect of gravity causing the object to fall, while the term 20t represents the initial upward velocity. The quadratic term, -4.9t², ensures that the path of the object follows a parabolic trajectory.
This equation is a real-life example of a quadratic function as it represents the motion of an object under constant acceleration.