QuestionThe figure shows that when a football is kicked, the nearest defensive player is 6 feet from the point of impact with the kicker's foot. The height of the punted football, , in feet, can be modeled by the following equation.
Determine whether the following statement makes sense or does not make sense, and explain your reasoning.
The given figure shows that a linear model provides a better description of the football's path than a quadratic model.
Studdy Solution
STEP 1
1. The height of the football, , is modeled by the quadratic equation .
2. A linear model would be of the form .
3. We need to determine if a linear model is a better fit than the given quadratic model for the football's path.
STEP 2
1. Understand the nature of the quadratic model.
2. Compare the characteristics of quadratic and linear models.
3. Evaluate the statement based on the comparison.
STEP 3
The given equation is a quadratic equation. This implies that the path of the football is a parabola, which typically represents a curved trajectory.
STEP 4
A quadratic model, such as the one given, includes a squared term (), which allows for the representation of a curved path, such as the arc of a football when punted.
A linear model, represented by , describes a straight line, which does not account for the curvature seen in projectile motion like a football's path.
STEP 5
Since the path of a punted football is typically parabolic due to gravity, a quadratic model is more appropriate for capturing the curvature of the trajectory.
The statement that a linear model provides a better description does not make sense because it would not accurately represent the curved path of the football.
The statement does not make sense because a linear model cannot capture the parabolic trajectory of a punted football, which is better described by a quadratic model.
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