Let's consider a scenario where a soccer ball is kicked straight up into the air. We can use the quadratic function \( y = -16t^2 + h_0 \), where \( h_0 \) represents the initial height from which the ball is kicked. For example, if the ball is kicked from a height of 3 feet, the function would be \( y = -16t^2 + 3 \). Here, the variable \( t \) represents the time in seconds after the ball is kicked. The constant value \(-16\) indicates the acceleration due to gravity (in feet per second squared), reflecting that the ball's height decreases over time until it finally reaches the ground when \( y = 0 \). To find out how long it takes for the ball to hit the ground, we can solve the equation \( 0 = -16t^2 + 3 \).
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
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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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