Suppose you are outside on a cloudy day, just after it has rained. In the distance, you see a Rainbow in the sky. After looking more closely, you see a Drone take off, increasing in height as it travels, and fly through the Rainbow moving left to right, crossing the Rainbow in two places.
Answer the following questions in relation to this scenario. Use the Image below to assist you.
1. According to the image above, and using the x and y-Intercepts of the Parabola (the red line). Identify the equation of the Rainbow, represented by the Parabola.
Remember to use correct Equation Notation and provide your answer in Expanded (General or Vertex) Form.
Equation of the Parabola (Rainbow):



Choose two points on the graph, both on the outside of the Rainbow, one on each side (left and right). Connecting the points with a straight line, envision this to be the path of the Drone (increasing in height as it moves left to right). This line should cross the path of the Rainbow in two locations.
Complete the xy-Table below.
The points you include should be:
the two points you picked (Points 1 and 2),
the two points representing where the Drone intersects the Rainbow (Points 3 and 4)
(Show your work below using Algebra),
Hint: It would be helpful to skip to question 3 before completing this portion of question 2.
Use Points 1 and 2 and find the equation of the line (path of the drone).
Then, use that equation to algebraically locate points that satisfy both equations (the parabola and the line).
One additional point of your choice, on the line (drone path) (Point 5).
3. Using any two points from your table, identify the equation that represents the path of the Drone.
(Show your work below using Algebra),

Based on the Graph and your Calculations, answer the following Questions.
What is the Domain and Range of the Rainbow (not the Parabola)?
Work and Answer:


What is the Domain and Range of the Drone (not the Line)?
Work and Answer:


Is the Domain and/or Range of the Rainbow different from the Domain and/or Range of the Parabola?
Why or Why Not?
Answer:


Is the Domain and/or Range of the Drone different from the Domain and/or Range of the Linear Equation?
Why or Why Not?
Answer: