From the graph below, we have the equation of the curve to be:
[tex]x=-6\text{ twice}[/tex]
Let us get the factors of the equation,
[tex]\begin{gathered} x=-6\text{ or x=-6} \\ x+6=0\text{ or x+6=0} \\ (x+6)(x+6)=0 \end{gathered}[/tex]
Let us now expand the factors,
[tex]y=(x+6)(x+6)[/tex][tex]\begin{gathered} y=x(x+6)+6(x+6) \\ y=x^2+6x+6x+36 \end{gathered}[/tex][tex]y=x^2+12x+36[/tex]
Hence, the factorization of the polynomial graphed is,
y = x^2 + 12x + 36.
