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

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

The factored equation of f(x) will be

$f(x)=-\frac{1}{18}(x+3)^2(x-2)^2$

Hence, the factored equation of f(x) is

$f(x)=-\frac{1}{18}(x+3)^2(x-2)^2$