1. **Problem Statement:** Greg launches a rocket straight up, and we have a table of its height $H(t)$ at various times $t$. We want to understand the rocket's motion using this data. 2. **Given Data:** - $H(0) = 0$ meters - $H(2.2) = 110$ meters - $H(6.6) = 198$ meters - $H(8.8) = 44$ meters - $H(13.2) = 0$ meters 3. **Goal:** Analyze the rocket's height over time, identify when it reaches maximum height, and understand its flight duration. 4. **Key Concept:** The rocket's height as a function of time $H(t)$ is typically modeled by a quadratic function due to constant acceleration from gravity: $$H(t) = -at^2 + bt + c$$ where $a > 0$ (gravity effect), $b$ is initial velocity, and $c$ is initial height. 5. **Observations:** - At $t=0$, $H=0$ so $c=0$. - The rocket reaches maximum height at $t=6.6$ seconds with $H=198$ meters. - The rocket returns to ground level at $t=13.2$ seconds. 6. **Maximum Height Time:** The vertex of the parabola is at $t = \frac{b}{2a}$. Given vertex time $t=6.6$, and total flight time $13.2$ seconds (which is twice the vertex time), this confirms symmetry. 7. **Summary:** The rocket rises to 198 meters at 6.6 seconds, then falls back to ground at 13.2 seconds. This analysis helps understand the rocket's flight path and timing.