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

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

Answer 2

The parabola graph can be drawn through the quadratic function. For the quadratic function, if $a<0$ then graph will open down and if $a>0$ graph will open upward.

Given:

The given parabola equation is $y=-x^2+36$.

Find the intersection point at $y$ for $x=1$

$y=-(1)^2+36\\y=35$

The points will be $(1,35)$.

Find the intersection point at $y$ for $x=2$.

$y=-(2)^2+36\\y=32$

The points will be $(2,32)$.

Find the intersection point at $y$ for $x=3$.

$y=-(3)^2+36\\y=25$

The points will be $(3,25)$.

Find the intersection point at $y$ for $x=6$.

$y=-(6)^2+36\\y=0$

The points will be $(6,36)$.

Thus, the intersection point will be $(6,36)$ and $(2,32)$.

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