Question

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.

y, equals, minus, 16, x, squared, plus, 242, x, plus, 84
y=−16x
2
+242x+84
y, equals, minus, 16, x, squared, plus, 242, x, plus, 84

Answer 1

Answer: Therefore, the rocket will reach its maximum height at around 7.56 seconds after launch.

Step-by-step explanation: To find the time at which the rocket will reach its maximum height, we need to use the vertex formula:

x = -b/2a

where a, b, and c are the coefficients of the quadratic equation. In this case, a = -16, b = 242, and c = 84.

Substituting these values into the formula:

x = -242/(2*(-16))

x = -242/-32

x ≈ 7.56 seconds

Therefore, the rocket will reach its maximum height at around 7.56 seconds after launch.