A long jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above and he ground. Write the equation of a parabola that models his path through the air, where x is horizontal distance from the start line in m and y is his height, in cm.

The equation of the parabola that models the path of the long jumper through the air is .

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

Where:

- Horizontal distance from the start line, measured in meters.

- Height of the long jumper, measured in meters.

, , - Polynomial constants, measured in , dimensionless and meters, respectively.

If we know that , and , this system of linear equations is presented below:

(Eq. 1)

(Eq. 2)

(Eq. 3)

The coefficients of the polynomial are, respectively:

, ,

The equation of the parabola that models the path of the long jumper through the air is .

But we need measured in centimeters, then, we use the following conversion:

Then, we get that:

Where and are measured in meters and centimeters, respectively.

The equation of the parabola that models the path of the long jumper through the air is .