3. Patrick kicks a soccer ball from the ground into the air. When the ball is a horizontal distance of 12 feet from him, it is 14 feet above the ground. When the ball is 32 feet from him, it is 7 feet above the ground.
Use quadratic regression on a graphing calculator to write a function for the height of the ball in terms of
its horizontal distance Round to the nearest thousandth (

The function for the height of the ball in terms of its horizontal distance is

Step-by-step explanation:

From Physics, we know that ball describes a parabolic motion, in which trajectory is described by the following second-order polynomial (quadratic function):

(Eq. 1)

Where:

- Horizontal distance, measured in feet.

- Vertical distance above the ground, measured in feet.

- Second order coefficient, measured in .

- First order coefficient, dimensionless.

- Zero order coefficient, measured in feet.

We can obtain the second-order polynomial associated with the soccer ball by knowing three distinct points and solving the resulting system of linear equations. If we know that , and , then the system of linear equations is:

The solution of this linear system is:

, ,

Therefore, the function for the height of the ball in terms of its horizontal distance is

In addition, we present a graphic of the given function as attachment.

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step-by-step explanation: