Question

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

Answer 1

Answer:

The equation of the parabola is given to be : y = -x² + 36

So, the airplane will cut the rainbow if the graph of the equation of airplane intersects the graph of rainbow.

Now, to find the equation of airplane :

The points through which airplane passes are : (1,0) and (0,2)

⇒ Equation : 2x + y = 2

This equation will  intersect the parabola at exactly two points.

And the points are the solution of these two equation :

(-4.916,11.832) and (6.916,-11.832)

The required table is :

x        -4.916       11.832

y         6.916      -11.832

Answer 2

Let x represent the height of the airplane and let y be the distance of the rainbow.

Using the expression y=-x²+36, we can generate a table where four values indicate the possible location that the airplane meet the rainbow:

Intersections are:
when x=2, y=32
when x=-1, y=35
when x=1, y=35
when x=4, y=20