Question
Jayeon is a goalkeeper for his city's soccer team. He created a table to track the height of the ball, in feet, as a function of time, in seconds, when he puts it. What type of function best models this scenario? (1 point)
Answers
GPT-4o mini
The situation described, where the height of a soccer ball is tracked as a function of time during a kick, is best modeled by a quadratic function. When a soccer ball is kicked, it follows a parabolic trajectory due to the effects of gravity. The height of the ball over time can be represented as a quadratic equation in the form:
\[ h(t) = -at^2 + bt + c \]
where \( h(t) \) is the height of the ball at time \( t \), \( a \), \( b \), and \( c \) are constants that depend on the initial conditions of the kick (such as the initial height, initial velocity, and the acceleration due to gravity).
In summary, the best model for the height of the soccer ball as a function of time is a quadratic function.
\[ h(t) = -at^2 + bt + c \]
where \( h(t) \) is the height of the ball at time \( t \), \( a \), \( b \), and \( c \) are constants that depend on the initial conditions of the kick (such as the initial height, initial velocity, and the acceleration due to gravity).
In summary, the best model for the height of the soccer ball as a function of time is a quadratic function.