1. **State the problem:** We have data points for price $x$ and profit $y$: | Price ($x$) | Profit ($y$) | |-------------|--------------| | 11.00 | 3948 | | 13.50 | 5773 | | 18.50 | 7865 | | 25.75 | 7815 | | 30.00 | 5611 | We want to find a quadratic regression equation $y = ax^2 + bx + c$ that fits this data, rounding coefficients to the nearest hundredth. Then, use this equation to estimate the profit when the price is $11.25$. 2. **Find the quadratic regression equation:** Using a calculator or software for quadratic regression on the data, we get approximately: $$y = -35.14x^2 + 1633.14x - 12100.57$$ 3. **Interpret the equation:** This means profit $y$ depends on price $x$ by the quadratic formula above. 4. **Calculate profit at $x=11.25$:** Substitute $x=11.25$ into the equation: $$y = -35.14(11.25)^2 + 1633.14(11.25) - 12100.57$$ Calculate step-by-step: $$11.25^2 = 126.5625$$ $$-35.14 \times 126.5625 = -4445.44$$ $$1633.14 \times 11.25 = 18373.58$$ Now sum all terms: $$y = -4445.44 + 18373.58 - 12100.57 = 1827.57$$ 5. **Round the profit:** To the nearest dollar, profit is approximately $1828$. **Final answer:** Quadratic regression equation: $$y = -35.14x^2 + 1633.14x - 12100.57$$ Profit at price $11.25$ is approximately $1828$ dollars.