Question

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.

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

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.

Answer 1

A function that can represent the ascent of the plane and cut the parabola in two points, can be given by the following table
X -10 -6 0 10
Y -24 0 36 96
The equation of the line for this table is
y = 6x + 36
Graphic attachment