#### Answer

It is a polynomial.
Degree: 2
Leading term: $-\frac{1}{2}x^2$
Constant: $\frac{1}{2}$
$g(x)=-\frac{1}{2}x^2 +\frac{1}{2}$

#### Work Step by Step

First, we rewrite the function to make it easier to examine:
$g(x)=-\frac{1}{2}x^2 +\frac{1}{2}$
By definition, a polynomial is a function containing only terms where x is raised to a power or constants. x is raised to the second power, and $\frac{1}{2}$ is a constant, so it is a polynomial. The degree is equal to the exponent of the term with the highest exponent, so the degree is 2. The term that has the highest degree, $\frac{1}{2}x^2$, is always the leading term. Finally, $\frac{1}{2}$ is the constant.