Question 9 (10 points) If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t)=-16t^2+128t (air resistance is neglected) How long did it take the toy rocket to reach its maximum height? 6 seconds b 4 seconds 2 seconds d 1 second

Question

Question 9 (10 points) If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t)=-16t^2+128t (air resistance is neglected) How long did it take the toy rocket to reach its maximum height? 6 seconds b 4 seconds 2 seconds d 1 second

Answer 1

The toy rocket reaches its maximum height after 4 seconds.

Answer 2

## Step 1The given equation is a quadratic equation in the form of

, where

,

, and

. The maximum height of the toy rocket is reached at the vertex of the parabola represented by this equation.## Step 2The x-coordinate of the vertex of a parabola given by the equation

is given by the formula

.### **The formula for the x-coordinate of the vertex is

**## Step 3Substitute the values of

and

into the formula to find the time

when the maximum height is reached.### **Substitute

and

into the formula to get \( t = -128/(2*-16) \)**

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