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.

2 answers

Let's consider the scenario of a soccer ball being kicked upwards into the air from a height of 3 feet. We can model the height of the soccer ball above the ground as a quadratic function using the formula \( y = -16t^2 + vt + h \), where \( v \) is the initial velocity (in feet per second) when the ball is kicked, and \( h \) is the initial height (in feet). For this example, let's assume the initial velocity of the ball is 20 feet per second. Therefore, the complete function becomes:

\[ y = -16t^2 + 20t + 3. \]

In this function, \( y \) represents the height of the soccer ball in feet, and \( t \) is the time in seconds after the ball has been kicked. The constant value of -16 represents the acceleration due to gravity in feet per second squared (the negative sign indicates that the height decreases over time), while the initial height \( h \) of 3 feet indicates the starting position from which the ball is kicked. To predict when the ball will hit the ground, we would set \( y = 0 \) and solve for \( t \).

can you write it like a kid