Write an equation for the polynomial graph: 01510102861.jpg y(x)=?

Question
Polynomial graphs
asked 2021-03-07
Write an equation for the polynomial graph:
image
y(x)=?

Answers (1)

2021-03-08
\(\displaystyle{x}_{{1}}=-{2},{x}_{{2}}=-{2},{x}_{{3}}={2},{x}_{{4}}={4}\)
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)
\(\displaystyle{y}{\left({x}\right)}=-\frac{{1}}{{16}}{\left({x}+{2}\right)}{\left({x}+{2}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}\)
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