8. Analyzing Graphs of Polynomial Functions
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Use the Zero Product Property to find the zeros of the polynomial function.
We want to graph the given polynomial function. h(x)=(x+1)^2(x-1)(x-3) Let's start by finding the zeros of the function.
Use the Zero Product Property
(I): sqrt(LHS)=sqrt(RHS)
(I): LHS-1=RHS-1
(II): LHS+1=RHS+1
(III): LHS+3=RHS+3
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+1)^2(x-1)(x-3) | h(x)=(x+1)^2(x-1)(x-3) |
---|---|---|
- 1.5 | ( - 1.5+1)^2( - 1.5-1)( - 1.5-3) | 2.813 |
-0.5 | ( - 0.5+1)^2( - 0.5-1)( - 0.5-3) | 1.313 |
0 | ( 0+1)^2( 0-1)( 0-3) | 3 |
2 | ( 2+1)^2( 2-1)( 2-3) | -9 |
(a+b)^2=a^2+2ab+b^2
Distribute x-1
Distribute x^2
Distribute 2x
Distribute 1
Subtract terms
Distribute (x-3)
Distribute x^3
Distribute x^2
Distribute - x
Distribute -1
Add and subtract terms