1. **Problem:** Find how long the rocket is in the air given the height function $$h = -16t^2 + 128t$$ where $h$ is height in feet and $t$ is time in seconds. 2. **Formula and rules:** The rocket is in the air from launch ($t=0$) until it hits the ground ($h=0$). To find the time in the air, solve for $t$ when $h=0$: $$-16t^2 + 128t = 0$$ 3. **Solve the equation:** Factor out $t$: $$t(-16t + 128) = 0$$ Set each factor equal to zero: $$t = 0 \quad \text{or} \quad -16t + 128 = 0$$ Solve the second equation: $$-16t + 128 = 0 \implies -16t = -128 \implies t = \frac{128}{16} = 8$$ 4. **Interpretation:** $t=0$ is the launch time, and $t=8$ seconds is when the rocket hits the ground. 5. **Answer:** The rocket is in the air for **8 seconds**.