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

Question

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 straight up into the air. We want to predict when the ball will return to the ground after being kicked. We can use the quadratic function \( y = -16t^2 + vt + h \), where \( v \) is the initial velocity of the ball in feet per second, and \( h \) is the initial height from which the ball was kicked. For this example, let's say the ball is kicked from ground level with an initial velocity of 32 feet per second. The complete function would then be \( y = -16t^2 + 32t \).

In this function, \( y \) represents the height of the ball in feet, and \( t \) represents the time in seconds after the ball is kicked. The constant value \(-16\) represents the acceleration due to gravity in feet per second squared, indicating that the ball's height decreases over time as it rises and then falls back down. To find when the ball returns to the ground, we can set \( y \) to 0 and solve for \( t \).