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=−16t2 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. :)

Answer 1

Let's consider a scenario where a soccer ball is kicked into the air from the height of 4 feet. The quadratic function that describes the height of the soccer ball over time is given by:

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

In this function, \( y \) represents the height of the ball above the ground in feet, while \( t \) represents the time in seconds after the ball has been kicked. The constant value \( 4 \) signifies the initial height from which the ball was kicked. The term \( -16t^2 \) illustrates the acceleration due to gravity, indicating that the ball will rise to a certain height before falling back to the ground. To find out when the ball will hit the ground, we can set \( y \) equal to zero and solve for \( t \).

Answer 2

can you write it like a kid

Answer 3

Sure! Imagine you kick a soccer ball from a height of 4 feet into the air. The height of the ball over time can be described by this function:

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

In this function, \( y \) is how high the ball is in feet, and \( t \) is how many seconds have passed since you kicked it. The \( 4 \) means the ball starts 4 feet off the ground. The \( -16t^2 \) part shows how gravity pulls the ball down. To find out when the ball hits the ground, we would set \( y \) equal to 0 and solve for \( t \). That tells us how long the ball stays in the air!