To find the x-intercepts, solve \(\displaystyle{f{{\left({x}\right)}}}={0}\)

\(\displaystyle{x}^{{{4}}}-{5}{x}^{{{2}}}+{6}={0}\)

\(\displaystyle{\left({x}^{{{2}}}-{3}\right)}{\left({x}^{{{2}}}-{2}\right)}={0}\) Factor the trinomial

\(\displaystyle{x}^{{{2}}}-{3}={0}\) or \(\displaystyle{x}^{{{2}}}-{2}={0}\) Set each factor equal to 0

\(\displaystyle{x}=\pm\sqrt{{{3}}}\) or \(\displaystyle{x}=\pm\sqrt{{{2}}}\) Solve each equation

So, the x-intercepts are \(\displaystyle{\left(\sqrt{{{3}}},{0}\right)},{\left(\sqrt{{{2}}},{0}\right)},{\left(-\sqrt{{{3}}},{0}\right)},{\left(-\sqrt{{{2}}},{0}\right)}\)

Step 2

To find the y-intercept evaluate \(\displaystyle{f{{\left({0}\right)}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{5}{x}^{{{2}}}+{6}\)

\(\displaystyle{f{{\left({0}\right)}}}={0}^{{{4}}}-{5}{\left({0}\right)}^{{{2}}}+{6}\) Substitute 0 for x

\(\displaystyle={6}\) Simplify

So, the y-intercept is \(\displaystyle{\left({0},{6}\right)}\)

Plot the points (-2,2) and (2,2)