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

Write an equation for the polynomial graph:

$y\left(x\right)=?$

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${x}_{1}=-2,{x}_{2}=-2,{x}_{3}=2,{x}_{4}=4$
then the factors of y(x)
$\left(x-{x}_{1}\right)\left(x-{x}_{2}\right)\left(x-{x}_{3}\right)\left(x-{x}_{4}\right)$
$\left(x-\left(-2\right)\right)\left(x-\left(-2\right)\right)\left(x-2\right)\left(x-4\right)$
$\left(x+2\right)\left(x+2\right)\left(x-2\right)\left(x-4\right)$
y intercept is (0,-2)
put y and x values for k calculation
$-2=k\left(0+2\right)\left(0+2\right)\left(0-2\right)\left(0-4\right)$
$-2=k32$
$k=-\frac{2}{32}=-\frac{1}{16}$
$k=-\frac{1}{6}$
Now put the value of k in y(x)
$y\left(x\right)=-\frac{1}{16}\left(x+2\right)\left(x+2\right)\left(x-2\right)\left(x-4\right)$