1. **Problem:** Identify which statement about the polynomial function $f(x) = -2x + \sqrt{3} x^2 - \frac{1}{2} x^4$ is not correct. 2. **Formula and rules:** - The leading coefficient is the coefficient of the term with the highest degree. - The constant term is the term without $x$. - The degree of a polynomial is the highest power of $x$. 3. **Step-by-step analysis:** - The polynomial is $f(x) = -2x + \sqrt{3} x^2 - \frac{1}{2} x^4$. - The highest degree term is $-\frac{1}{2} x^4$, so the leading coefficient is $-\frac{1}{2}$, not $\frac{1}{2}$. - The constant term is $0$ because there is no term without $x$. - The degree is $4$, not $3$. - The leading term is $-\frac{1}{2} x^4$, not $\frac{1}{2} x^4$. 4. **Conclusion:** - Option A says the leading coefficient is $\frac{1}{2}$, which is incorrect. - Option B is correct. - Option C is incorrect in wording but the degree is $4$, not $3$. - Option D is incorrect because the leading term has coefficient $-\frac{1}{2}$, not $\frac{1}{2}$. **Final answer:** The statement that is not correct is **A**.