Let's consider a scenario where a soccer ball is kicked into the air from an even surface. We can use the quadratic function \( y = -16t^2 + vt + h \) to model the height \( y \) of the ball over time \( t \) seconds after it has been kicked. Here, \( v \) represents the initial velocity with which the ball was kicked (in feet per second), and \( h \) represents the initial height from which the ball is kicked (in feet). If we assume the ball is kicked from ground level with an initial velocity of 32 feet per second, the complete function would be \( y = -16t^2 + 32t \). The variable \( t \) represents the time in seconds, while the constant value \( -16 \) denotes the acceleration due to gravity (in feet per second squared), which affects how quickly the ball falls back to the ground after reaching its peak height. To find out when the ball will hit the ground, we can set \( y = 0 \) and solve for \( t \).
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)
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