Answer:
We are given that,
The equation of the rainbow is represented by the parabola,
![y=-x^2+36](https://tex.z-dn.net/?f=y%3D-x%5E2%2B36)
Now, we are required to find a linear equation which cuts the graph of the parabola at two points.
Let us consider the equation joining the points (-6,0) and (0,36), given by
.
So, the corresponding table for the linear equation is given by,
x ![y=6x+36](https://tex.z-dn.net/?f=y%3D6x%2B36)
-6 0
0 36
1 42
6 72
Now, we will answer the questions corresponding the functions.
1. Domain and Range of the rainbow.
Since, the equation of the rainbow is ![y=-x^2+36](https://tex.z-dn.net/?f=y%3D-x%5E2%2B36)
So, from the figure, we get that,
Domain is the set of all real numbers.
Range is the set ![\{ y|y\leq 36 \}](https://tex.z-dn.net/?f=%5C%7B%20y%7Cy%5Cleq%2036%20%5C%7D)
<em>Here, domain represents the points which are used to plot the path of the rainbow and range represents the points which are form the rainbow.</em>
Not all points make sense in the range as the parabola is opening downwards having maximum point as (0,36).
2. X and Y-intercepts of the rainbow.
<em>As, the 'x and y-intercepts are the points where the graph of the function cuts x-axis and y-axis respectively i.e. where y=0 and x=0 receptively'.</em>
We see that from the figure below,
X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)
<em>Here, these intercepts represents the point where the parabola intersects the individual axis.</em>
3. Is the linear function positive or negative.
As the linear function is
represented by the <em>upward flight of the drone.</em>
So, the linear function is a positive function.
4. The solution of the system of equations is the intersection points of their graphs.
So, from the figure, we see that the equations intersect at the points (-6,0) and (0,36).
<em>Thus, the solution represents the position when both the drone and rainbow intersect each other.</em>