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=-16x^2+171x+87

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=-16x^2+171x+87

Answer 1

### The rocket will reach its maximum height at approximately 5.34 seconds.

Answer 2

## Step 1: Identify the equation### The height

as a function of time

is given by

.## Step 2: Find the time to reach the maximum height### To find the time at which the rocket reaches its maximum height, use the formula for the vertex of a parabola given by

. The time

at the vertex is

, where

and

.## Step 3: Calculate the time### Substitute

and

into the vertex formula:

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=-16x^2+171x+87

Answer

Answer

Explanation