Graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. courtesy of texas instruments in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent

All in the Explanation

Step-by-step explanation:

Vertex of the Parabola=(0,36)

X-Intercepts are (-6,0) and (0,6)

An equation with roots 6 and -6 is determined below;

x=6 or x=-6

(x-6)(x+6)=0

The two points of the slanted line cutting through the parabola are (-6,0) and (3,27).

First, we determine the equation of the line.

The slope of a line passing through the two points  and  is given by

We have that

Plug the given values into the formula for slope:

Now, the y-intercept is  the result is the same).

Finally, the equation of the line can be written in the form

f(x)=3x+18.

The linear function  y=3x+18 is positive since its slope, m is positive.

The system of equation created by the parabola and the curve is determined below:

The solution of the system . They represent the point of intersections of the curve and parabola.

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.