Question

A rocket is launched from the ground. The path that the rocket travels is modeled by the expression −x2+14x−40
where the x-axis represents the ground and the x-values are expressed in feet.

Select all of the statements that are correct about the rocket.

(2 points)
Responses

The rocket traveled a distance of 3 feet through the air.
The rocket traveled a distance of 3 feet through the air.

The maximum height of the rocket is 14 feet.
The maximum height of the rocket is 14 feet.

The rocket traveled a distance of 6 feet through the air.
The rocket traveled a distance of 6 feet through the air.

The maximum height of the rocket is 9 feet.

Answer 1

Correct choices:

- The rocket traveled a distance of 6 feet through the air.
- The maximum height of the rocket is 9 feet.

Work:
- Solve -x^2 + 14x - 40 = 0: roots x = 4 and x = 10, so horizontal distance = 10 − 4 = 6 ft.
- Vertex x = -b/(2a) = -14/(2·-1) = 7; y(7) = -(7)^2 + 14·7 − 40 = 9 ft.