A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.8x^2+12x+25.8 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.

Question

How far horizontally from its starting point will the rocket land? Round your answer to the nearest hundredth.

Answer 1

The rocket will land when it hits the ground, meaning y = 0. Therefore, we can set the equation equal to 0 and solve for x:

-0.8x^2 + 12x + 25.8 = 0

Using the quadratic formula, we get:

x = (-12 ± sqrt(12^2 - 4(-0.8)(25.8))) / (2(-0.8))
x = (-12 ± sqrt(584.64)) / (-1.6)

x ≈ -1.29 or x ≈ 15.79

Since the rocket was launched from a roof, we can disregard the negative solution. Therefore, the rocket will land approximately 15.79 meters horizontally from its starting point on the roof. Rounded to the nearest hundredth, this is 15.78 meters.

Answer 2

See the correct solution in the post above this

Answer 3

I apologize, you are correct. The correct solution is already given above.