I’m working on a Algebra exercise and need support.
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.
- 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.
- 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).
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