then the factors of y(x)

\(\displaystyle{\left({x}-{x}_{{1}}\right)}{\left({x}-{x}_{{2}}\right)}{\left({x}-{x}_{{3}}\right)}{\left({x}-{x}_{{4}}\right)}\)

\(\displaystyle{\left({x}-{\left(-{2}\right)}\right)}{\left({x}-{\left(-{2}\right)}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}\)

\(\displaystyle{\left({x}+{2}\right)}{\left({x}+{2}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}\)

y intercept is (0,-2)

put y and x values for k calculation

\(\displaystyle-{2}={k}{\left({0}+{2}\right)}{\left({0}+{2}\right)}{\left({0}-{2}\right)}{\left({0}-{4}\right)}\)

\(\displaystyle-{2}={k}{32}\)

\(\displaystyle{k}=-\frac{{2}}{{32}}=-\frac{{1}}{{16}}\)

\(\displaystyle{k}=-\frac{{1}}{{6}}\)

Now put the value of k in y(x)

\(\displaystyle{y}{\left({x}\right)}=-\frac{{1}}{{16}}{\left({x}+{2}\right)}{\left({x}+{2}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}\)