I need help using (6,0) (0,36) as the solutions. I'm not sure how to make a piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Here is the assignment and I'm stuck on the last question

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.

The equation for this parabola is y = -x2+ 36.

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.

x y

6 0

3 27

2 32

0 36

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?

The domain of the rainbow is (-6,6) and the range of the rainbow is (0,36). The domain represents the set of all possible x-value, which will make the function work and will output real y-values. The range is the value between the two points. The values in this situation do make sense because 36 is the maximum output and -6 and 6 are the endpoints.

What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.

The x intercepts are (-6,6) and represent the rainbow endpoints and the y intercepts are (0,36) which represent the rainbows highest point.

Is the linear function you created with your table positive or negative? Explain.

The linear function is positive because the slope is increasing.

What are the solutions or solution to the system of equations created? Explain what it or they represent.

(6,0) (0,36) are the solutions and they represent where the drone will intersect the rainbow.

Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).