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)=1/12(x+4)(x+8)(x-1) Let's start by finding the zeros of the function.
Use the Zero Product Property
(I): LHS-4=RHS-4
(II): LHS-8=RHS-8
(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 | 1/12(x+4)(x+8)(x-1) | g(x)=1/12(x+4)(x+8)(x-1) |
---|---|---|
-7 | 1/12( -7+4)( -7+8)( -7-1) | 2 |
-5 | 1/12( -5+4)( -5+8)( -5-1) | 1.5 |
-2 | 1/12( -2+4)( -2+8)( -2-1) | -3 |
0 | 1/12( 0+4)( 0+8)( 0-1) | ≈ - 2.67 |
Distribute (x-1)
Distribute x
Distribute 8
Subtract term
Distribute (x+4)
Distribute x^2
Distribute 7x
Distribute 8
Subtract terms
Distribute 1/12