1. **State the problem:** Simplify the function $F(x) = x^2 - 12x^2 + 36x - 1$. 2. **Combine like terms:** The terms $x^2$ and $-12x^2$ are like terms. 3. **Simplify the quadratic terms:** $$x^2 - 12x^2 = (1 - 12)x^2 = -11x^2$$ 4. **Rewrite the function:** $$F(x) = -11x^2 + 36x - 1$$ 5. **Final simplified form:** $$F(x) = -11x^2 + 36x - 1$$ This is a quadratic function in standard form with coefficients $a = -11$, $b = 36$, and $c = -1$.