Question

I have a picture of a graph and I need to write the equation for a degree four polynomial

Answer 1

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,

`(x+3),(x+1),(x-3),(x-4)`

The polynomial is,

`p(x)=a(x+3)(x+1)(x-3)(x-4)`

to determine the sketch factor use the y-intercept point.

(0,1).

`\begin{gathered} p(0)=a(0+3)(0+1)(0-3)(0-4) \\ 1=a(3)(1)(-3)(-4)_{} \\ 1=a\cdot36 \\ a=(1)/(36) \end{gathered}`
`p(x)=(1)/(36)(x+3)(x+1)(x-3)(x-4)`