Step 1

The given function is,

\(g(x)=3-\frac{x^{2}}{4}\ or\ g(x)=-\frac{1}{4}x^{2}+3\).

From the definition of polynomial function, it can be said that, the given function is a polynomial function.

The highest power of x in the expression \(3-\frac{x^{2}}{4}\) is 2.

Thus, degree of the polynomial is 2.

Step 2

The standard form of a polynomial function is,

\(g(x)=a_{2}x^{2}+a_{1}x+a_{0},\ where\ a_{2}=-\frac{1}{4}, a_{1}=0\ and\ a_{0}=3\)

\(\Rightarrow g(x)=-\frac{1}{4}x^{2}+3\)