After a dreary day of rain, the sun peeks through the clouds and rainbow forms. you notice the rainbow is the shape of a parabola.
the equation for this parabola is y = -x^2 + 36.
graph of a parabola opening down at the vertex 0 commas 36 crossing the x–axis at negative 6 commas 0 and 6 commas 0.
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.
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 positive or negative? explain.
what are the solutions or solution to the system of equations created? explain what it or they represent.

In the picture attached, both the plot of the parabola and of the straight line are shown. The parabola represents the rainbow and the line, the path of the drone.  

Drone path

xy

-511

-415

031

135

What is the domain and range of the rainbow? Explain what the domain and range represent.  

The domain of a parabola is all real numbers, the range of this parabola is [-infinite, 36].   The domain represents all possible values x-variable can take. The range represents all possible values y-variable can take.

Do all of the values make sense in this situation? Why or why not?

No, it doesn't. Only values between [0, 36] of the range make sense, because negative values are below the horizon, where there is no rainbow

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

x-intercepts: (-6, 0) and (0, 6). They represent the points at which the rainbow intercept the horizon.

y-intercepts: (0, 36). It represents the maximum height of the rainbow.

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

The linear function created has a positive slope. As a consequence, the function is always increasing.

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

The solutions are the points at which the parabola and the line intercept. In this case they are points (-5, 11) and (1,35)

bottom left

step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

hope this !

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step-by-step explanation: