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

The maximum height of the rocket is 9 feet.
The maximum height of the rocket is 9 feet.

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

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

Answer 1

Correct answers:

- The maximum height of the rocket is 9 feet.
- Vertex: x = -b/(2a) = -14/(2·-1) = 7; y = -(7)^2 + 14·7 - 40 = 9.

- The rocket traveled a distance of 6 feet through the air.
- Roots: -x^2 + 14x - 40 = 0 → x^2 - 14x + 40 = 0 → (x-4)(x-10)=0, so x = 4 and 10; distance = 10 − 4 = 6 feet.