06.04 Graphing Systems of Nonlinear Equations PDF

Preview

Summary

You have to graph systems that are nonlinear equations and then you can submit. I got a 100% so I really hope that this helps....

Description

Directions: Please type your responses to each question in a different color (red, blue, green, etc) to make it easier to read.

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.

1. 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 -6 4 0 2

y 0 20 12 16

2. Analyze the two functions. Answer the following reflection questions in complete sentences. a. 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 all real numbers. The range is negative infinity to positive 36. The domain represents the width of the Rainbow, and the range is the height the rainbow is. No, the values do not make sense because you cannot have a negative height or width. b. What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. The x-intercepts are at (-6,0) and (6,0) and the y- intercept is at (0,36). The x-interval is the rainbow meeting the horizon and the y-interval is the height from horizon up into the sky. c. Is the linear function you created with your table positive or negative? Explain. The linear function created by the table is positive because it is a rainbow going up making it a positive slope. d. What are the solutions or solution to the system of equations created? Explain what it or they represent. The solutions of the systems are (-6,0) and (4,20) 3. 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) f(x)=x+3, x>0 f(x)= 2x2, x≤0 First thing you do is plot the y intercept of the 1st equation, use the slope to create the next point, starting at x=0 or x>0. Then for next equation start with any points after that....