1. **State the problem:** We need to find the value of the function $f(x) = -x^2 + 3x - 1$ at $x = -4$. 2. **Write the formula:** The function is given by $$f(x) = -x^2 + 3x - 1$$ 3. **Substitute $x = -4$ into the function:** $$f(-4) = -(-4)^2 + 3(-4) - 1$$ 4. **Calculate the square:** $$(-4)^2 = 16$$ 5. **Substitute and simplify:** $$f(-4) = -16 + 3(-4) - 1$$ 6. **Multiply:** $$3(-4) = -12$$ 7. **Simplify the expression:** $$f(-4) = -16 - 12 - 1$$ 8. **Add the terms:** $$-16 - 12 = -28$$ $$-28 - 1 = -29$$ **Final answer:** $$f(-4) = -29$$