Question

A rocket is launched from ground level directly upward at a rate of 64 feet per second. The equation for the rocket's height is y = -16x² + 64x. When will the rocket be at or above a height of 48 feet?

A) x = 1 second
B) x = 2 seconds
C) x = 3 seconds
D) x = 4 seconds

Answer 1

The rocket will be at or above a height of 48 feet at x = 1 second and x = 3 seconds.

Step-by-step explanation:

To find when the rocket will be at or above a height of 48 feet, we need to solve the equation y = -16x² + 64x for x when y = 48. Substituting y = 48 into the equation, we get 48 = -16x² + 64x.

Rearranging the equation, we get 16x² - 64x + 48 = 0. Factoring the equation, we have 16(x - 1)(x - 3) = 0.

Setting each factor equal to zero, we find that x = 1 or x = 3. Therefore, the rocket will be at or above a height of 48 feet at x = 1 second and x = 3 seconds.