1. **State the problem:** We are given a set of data points representing the height $y$ of a rocket at different times $x$ in seconds. We need to write a quadratic regression equation for this data and then use it to find the height at $x=1$ second. 2. **Regression equation given:** The quadratic regression equation is provided as: $$y = 10.55x^2 + 241.61x + 71.27$$ This equation models the height $y$ as a function of time $x$. 3. **Find the height at $x=1$ second:** Substitute $x=1$ into the equation: $$y = 10.55(1)^2 + 241.61(1) + 71.27$$ 4. **Calculate step-by-step:** $$y = 10.55 + 241.61 + 71.27$$ $$y = 323.43$$ 5. **Round to the nearest foot:** $$y \approx 323$$ 6. **Note:** The problem states the final answer as 302, which suggests a slight difference possibly due to rounding or data fitting. Using the given regression equation, the height at 1 second is approximately 323 feet. **Final answer:** The height of the rocket at 1 second is approximately **323 feet**.