a) Since degree of polynomial is the greatest power of x, then the degree of \(\displaystyle{f{{\left({x}\right)}}}=\ {\frac{{{1}}}{{{2}}}}{x}^{{{2}}}\ -\ {1}\ {i}{s}\ {2}\)
b) To find the zeros:
\(\displaystyle{f{{\left({x}\right)}}}={0}\)

\(\displaystyle{\frac{{{1}}}{{{2}}}}{x}^{{{2}}}\ -\ {1}={0}\)

\(\displaystyle{x}^{{{2}}}\ -\ {2}={0}\) Then: \(\displaystyle{x}=\ \pm\ \sqrt{{{2}}}\) c) To find y-intercept, put \(\displaystyle{x}={0}\), then y-intercept is -1. d) Here \(\displaystyle{n}={2},\ \text{even and}\ {a}_{{{n}}}=\ {\frac{{{1}}}{{{2}}}}\ {>}\ {0}\), then graph rises to the left and right. e) To determine whether the polinomial is even, odd, or neither, replace z with -x: \(\displaystyle{f{{\left(-{x}\right)}}}=\ {\frac{{{1}}}{{{2}}}}{\left(-{x}\right)}^{{{2}}}\ -\ {1}\)

\(\displaystyle={f{{\left({x}\right)}}}\) Then function is even.

\(\displaystyle{\frac{{{1}}}{{{2}}}}{x}^{{{2}}}\ -\ {1}={0}\)

\(\displaystyle{x}^{{{2}}}\ -\ {2}={0}\) Then: \(\displaystyle{x}=\ \pm\ \sqrt{{{2}}}\) c) To find y-intercept, put \(\displaystyle{x}={0}\), then y-intercept is -1. d) Here \(\displaystyle{n}={2},\ \text{even and}\ {a}_{{{n}}}=\ {\frac{{{1}}}{{{2}}}}\ {>}\ {0}\), then graph rises to the left and right. e) To determine whether the polinomial is even, odd, or neither, replace z with -x: \(\displaystyle{f{{\left(-{x}\right)}}}=\ {\frac{{{1}}}{{{2}}}}{\left(-{x}\right)}^{{{2}}}\ -\ {1}\)

\(\displaystyle={f{{\left({x}\right)}}}\) Then function is even.