1. **State the problem:** We need to find the value of the function $K(x) = 2x^2 - 5x + 3$ when $x = -3$. 2. **Formula used:** The function is given by $$K(x) = 2x^2 - 5x + 3$$ To find $K(-3)$, substitute $x = -3$ into the function. 3. **Substitute and simplify:** $$K(-3) = 2(-3)^2 - 5(-3) + 3$$ Calculate each term: $$(-3)^2 = 9$$ So, $$K(-3) = 2 \times 9 - 5 \times (-3) + 3$$ 4. **Multiply:** $$K(-3) = 18 + 15 + 3$$ 5. **Add all terms:** $$K(-3) = 18 + 15 + 3 = 36$$ 6. **Final answer:** $$\boxed{36}$$ Therefore, the value of $K(-3)$ is 36, which corresponds to option 2.