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.(4 points)

Answer 1

Let's consider a scenario in which a soccer ball is kicked from a height of 4 feet above the ground. The quadratic function that describes the ball's height \(y\) in feet at time \(t\) in seconds after the kick can be expressed as:

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

In this function, \(t\) represents the time in seconds since the ball was kicked, while the constant value \(4\) indicates the initial height from which the ball was kicked. The term \(-16t^2\) reflects the effect of gravity on the ball's height, with the negative coefficient indicating that the height decreases over time due to the downward acceleration. We can use this function to determine the time it takes for the ball to return to the ground by setting \(y\) to 0 and solving for \(t\).