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

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

Answer 1

Correct statements:
- The maximum height of the rocket is 9 feet.
- Vertex: x = -b/(2a) = -14/(2·-1) = 7. f(7) = −7^2 + 14·7 − 40 = −49 + 98 − 40 = 9.
- The rocket traveled a distance of 6 feet through the air.
- Zeros: −x^2 + 14x − 40 = 0 ⇒ x^2 − 14x + 40 = 0 ⇒ (x−4)(x−10)=0, so it lands at x = 10 after launching at x = 4. Distance = 10 − 4 = 6 ft.

The statements “maximum height 14 feet” and “traveled 3 feet” are incorrect.