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. f(x)=(x+2)^2(x+4)^2 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): sqrt(LHS)=sqrt(RHS)
(II): LHS-4=RHS-4
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+4)^2 | f(x)=(x+2)^2(x+4)^2 |
---|---|---|
- 5 | ( - 5+2)^2( - 5+4)^2 | 9 |
- 3 | ( - 3+2)^2( - 3+4)^2 | 1 |
- 1 | ( - 1+2)^2( - 1+4)^2 | 9 |
(a+b)^2=a^2+2ab+b^2
Calculate power and product
Distribute (x^2+8x+16)
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