**6.05 Graphing Systems of Nonlinear Equations**

Nakayla Spencer

Nakayla Spencer

3.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?

2.Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function. Remember to include the two points of intersection in your table.

3.Analyze the two functions. Answer the following reflection questions in complete sentences.

•Is the linear function you created positive or negative? Explain.

Y=4x+24

This linear function is positive. It is positive because the line on the graph is going up not down.

3.Analyze the two functions. Answer the following reflection questions in complete sentences.

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

**Option 1: Work alone**

**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.**

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

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

-6,0 First Coordinates

2,32 Second Coordinates

32-0

2-(-6)

32

8

4

=

=

**y=4x+24**

(2,32)

X

-6

0

1

2

Y

0

24

28

32

D: [-6,6]

-6<X<6

R: [0,36]

0<X<36

The range represents how high above ground the rainbow would be.

The domain represents how far east west the rainbow would be.

X-intercepts:-6 and 6

Y-intercept: 36

Yes, all of the values make sense in this situation. The reason is that the range is all positive numbers, if the range had a negative number it would be incorrect because a rainbow can not go underground.

Yes, all of the values make sense in this situation. The reason is that the domain goes from negative to positive, a rainbow reaches from point A to point B. Which in this case is -6 and 6.

3.Analyze the two functions. Answer the following reflection questions in complete sentences.

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

The two X-intercepts represents where the rainbow meets the grount at -6 and meets the ground again at 6.

The Y-intercept represents how high in the sky the rainbow goes at 36.

(2,32)

(2,32)

There are two solutions.

Solution 1: (-6,0)

Solution 2: (2,32)

They represent where the drone crosses the rainbow.

(1,28)

(0,24)

(0,24)