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
y
=
−
16
t
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)
BoldItalicUnderlineIncrease indentDecrease indentFormula
y
=
−
16
t
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)
BoldItalicUnderlineIncrease indentDecrease indentFormula
Answers
GPT-4o mini
In a scenario where a ball is kicked into the air, we can use the quadratic function \( y = -16t^2 + vt + h \) to predict the ball's height over time, where \( v \) represents the initial velocity (in feet per second) at which the ball is kicked, and \( h \) is the initial height (in feet) from which the ball is kicked. For example, if the ball is kicked with an initial velocity of 32 feet per second from a height of 5 feet, the function would be written as \( y = -16t^2 + 32t + 5 \). In this function, \( t \) represents the time (in seconds) since the ball was kicked, while the constant value of \(-16\) is the acceleration due to gravity, which affects the ball's descent. To find when the ball returns to the ground, we can solve for \( t \) when \( y = 0 \).
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GPT-4o mini
Sure! Here’s the response with the numbers formatted in a computer font style:
In a scenario where a ball is kicked into the air, we can use the quadratic function \( y = -16t^2 + vt + h \) to predict the ball's height over time, where \( v \) represents the initial velocity (in feet per second) at which the ball is kicked, and \( h \) is the initial height (in feet) from which the ball is kicked. For example, if the ball is kicked with an initial velocity of **32** feet per second from a height of **5** feet, the function would be written as \( y = -16t^2 + 32t + 5 \). In this function, \( t \) represents the time (in seconds) since the ball was kicked, while the constant value of **-16** is the acceleration due to gravity, which affects the ball's descent. To find when the ball returns to the ground, we can solve for \( t \) when \( y = 0 \).
In a scenario where a ball is kicked into the air, we can use the quadratic function \( y = -16t^2 + vt + h \) to predict the ball's height over time, where \( v \) represents the initial velocity (in feet per second) at which the ball is kicked, and \( h \) is the initial height (in feet) from which the ball is kicked. For example, if the ball is kicked with an initial velocity of **32** feet per second from a height of **5** feet, the function would be written as \( y = -16t^2 + 32t + 5 \). In this function, \( t \) represents the time (in seconds) since the ball was kicked, while the constant value of **-16** is the acceleration due to gravity, which affects the ball's descent. To find when the ball returns to the ground, we can solve for \( t \) when \( y = 0 \).
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GPT-4o mini
In a scenario where a ball is kicked into the air, we can use the quadratic function \( y = -16t^2 + vt + h \) to predict its height over time. If the ball is kicked with an initial velocity of **32** feet per second from a height of **5** feet, the function is \( y = -16t^2 + 32t + 5 \). Here, \( t \) represents the time (in seconds) since the ball was kicked, and **-16** is the acceleration due to gravity. We can determine when the ball returns to the ground by solving for \( t \) when \( y = 0 \).