Quadratic functions can be used to describe the rate at which an object will fall and predict when it will land or how high it may go. Create a quadratic function using the function y=−16t^2

Question

Quadratic functions can be used to describe the rate at which an object will fall and predict when it will land or how high it may go. Create a quadratic function using the function  y=−16t^2
  to help predict when an object will return to the ground from being kicked, dropped, or thrown. In 3–5 sentences, describe the scenario in which you will use the function. Write the complete function and explain the meaning of the variable t and the constant value.

GPT-4o mini · Answer

Let's consider a scenario where a soccer ball is kicked into the air from a height of 4 feet. In this case, we can use the quadratic function to model the height of the ball over time:

\[ y = -16t^2 + 4 \]

In this function, \( y \) represents the height of the soccer ball in feet, and \( t \) represents the time in seconds since the ball was kicked. The constant value \( 4 \) signifies the initial height from which the ball is kicked, while the coefficient \(-16\) represents the acceleration due to gravity (in feet per second squared), indicating how quickly the ball descends. To find when the ball will hit the ground, we can set \( y = 0 \) and solve the equation for \( t \).