1. **State the problem:** We are given the height of a rocket as a function of time: $$h = -3t^2 + 24t$$ where $h$ is the height in meters and $t$ is the time in seconds. 2. **Determine what is asked:** We need to find the times $t$ when the rocket is 45 meters high. 3. **Set up the equation:** To find the times when the height is 45 meters, set $$h = 45$$: $$-3t^2 + 24t = 45$$ 4. **Rewrite the equation:** Move all terms to one side: $$-3t^2 + 24t - 45 = 0$$ 5. **Simplify the equation:** Divide the entire equation by $-3$ to simplify: $$\cancel{-3}t^2 + \cancel{-3}\times(-8)t + \cancel{-3}\times 15 = 0 \Rightarrow t^2 - 8t + 15 = 0$$ 6. **Factor the quadratic:** Find two numbers that multiply to 15 and add to -8: $$(t - 3)(t - 5) = 0$$ 7. **Solve for $t$:** Set each factor equal to zero: $$t - 3 = 0 \Rightarrow t = 3$$ $$t - 5 = 0 \Rightarrow t = 5$$ 8. **Interpret the result:** The rocket is 45 meters high at $t = 3$ seconds and $t = 5$ seconds. **Therefore, the rocket reaches a height of 45 meters at 3 seconds and again at 5 seconds.**