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 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be