To find the polynomial equation of the graph.
Now, identify the x-intercept of the graph,
x=-3 , x=-1 , x=3, x=4.
these are the factors of the polynomial,
[tex](x+3),(x+1),(x-3),(x-4)[/tex]
The polynomial is,
[tex]p(x)=a(x+3)(x+1)(x-3)(x-4)[/tex]
to determine the sketch factor use the y-intercept point.
(0,1).
[tex]\begin{gathered} p(0)=a(0+3)(0+1)(0-3)(0-4) \\ 1=a(3)(1)(-3)(-4)_{} \\ 1=a\cdot36 \\ a=\frac{1}{36} \end{gathered}[/tex][tex]p(x)=\frac{1}{36}(x+3)(x+1)(x-3)(x-4)[/tex]
