Question

Check PictureThe graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored equation for f(x).A quartic curve on a coordinate plane.

Answer 1

Soluion:

Given a graph of function f(x) with a degree of 4

Where theszeros of the graph polynomial are

`x=-3,2`

The function becomes

`f(x)=A(x+3)^2(x-2)^2`
`\begin{gathered} Where\text{ x}=0 \\ f(0)=-2 \end{gathered}`

Substitute for f(0) = -2 to find the value of A

`\begin{gathered} f(x)=A(x+3)^2(x-2)^2 \\ -2=A(0+3)^2(0-2)^2 \\ -2=A(3)^3(-2)^2 \\ -2=A(9)(4) \\ -2=A(36) \\ -2=36A \\ 36A=-2 \\ Divide\text{ both sides by 36} \\ (36A)/(36)=(-2)/(36) \\ A=-(1)/(18) \end{gathered}`

The factored equation of f(x) will be

`f(x)=-(1)/(18)(x+3)^2(x-2)^2`

Hence, the factored equation of f(x) is

`f(x)=-(1)/(18)(x+3)^2(x-2)^2`