1. **State the problem:** Amy's toy rocket is launched straight up, and its height over time is modeled by a downward-opening parabola. We need to find when the rocket is on the ground, its maximum height, when it reaches that height, and approximate its height at 1 second. 2. **Formula and rules:** The height $h(t)$ of a projectile launched upward can be modeled by a quadratic function: $$h(t) = -at^2 + bt + c$$ where $a > 0$ because the parabola opens downward, $b$ is the initial velocity term, and $c$ is the initial height (here $c=0$ since it starts from the ground). 3. **Given data from the graph:** - The rocket starts at ground level: $h(0) = 0$ - The rocket reaches maximum height around $t = 1.5$ seconds with height about $11$ meters - The rocket returns to ground near $t = 3$ seconds 4. **When is the rocket on the ground?** The rocket is on the ground when $h(t) = 0$. From the graph, this happens at $t=0$ and $t=3$ seconds. 5. **Maximum height and time:** The vertex of the parabola gives the maximum height. From the graph, the vertex is at approximately $t = 1.5$ seconds with height $h(1.5) = 11$ meters. 6. **Approximate height at 1 second:** From the graph, at $t=1$ second, the height is about $9$ meters. **Final answers:** - The rocket is on the ground at $t=0$ seconds and $t=3$ seconds. - The maximum height is approximately $11$ meters. - The rocket reaches its highest point at about $1.5$ seconds. - The height at $1$ second is approximately $9$ meters.