8. Analyzing Graphs of Polynomial Functions
Sign In
Use the Zero Product Property to find the zeros of the polynomial function.
We want to graph the given polynomial function. f(x)=(x-2)^2(x+1) Let's start by finding the zeros of the function.
Use the Zero Product Property
(I): sqrt(LHS)=sqrt(RHS)
(I): LHS+2=RHS+2
(II): LHS-1=RHS-1
To draw the graph of the function, we will find some additional points and consider the end behavior. Let's use a table to find additional points.
x | (x-2)^2(x+1) | f(x)=(x-2)^2(x+1) |
---|---|---|
- 0.5 | ( - 0.5-2)^2( - 0.5+1) | 3.125 |
0 | ( 0-2)^2( 0+1) | 4 |
1 | ( 1-2)^2( 1+1) | 2 |
3 | ( 3-2)^2( 3+1) | 4 |
(a+b)^2=a^2+2ab+b^2
Calculate power and product
Distribute (x+1)
Distribute x^2
Distribute - 4x
Distribute 4
Add and subtract terms