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. g(x)=4(x+1)(x+2)(x-1) Let's start by finding the zeros of the function.
Use the Zero Product Property
(I): LHS-1=RHS-1
(II): LHS-2=RHS-2
(III): 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 | 4(x+1)(x+2)(x-1) | g(x)=4(x+1)(x+2)(x-1) |
---|---|---|
- 1.5 | 4( - 1.5+1)( - 1.5+2)( - 1.5-1) | 2.5 |
- 0.5 | 4( - 0.5+1)( - 0.5+2)( - 0.5-1) | - 4.5 |
0 | 4( 0+1)( 0+2)( 0-1) | - 8 |
0.5 | 4( 0.5+1)( 0.5+2)( 0.5-1) | - 7.5 |
Distribute (x-1)
Distribute x
Distribute 2
Add terms
Distribute x+1
Distribute x^2
Distribute x
Distribute -2
Add and subtract terms
Distribute 4