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)= 1/3(x-5)(x+2)(x-3) Let's start by finding the zeros of the function.41
Use the Zero Product Property
(I): LHS+5=RHS+5
(II): LHS-2=RHS-2
(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 | 1/3(x-5)(x+2)(x-3) | h(x)= 1/3(x-5)(x+2)(x-3) |
---|---|---|
- 1 | 1/3( - 1-5)( - 1+2)( - 1-3) | 8 |
0 | 1/3( 0-5)( 0+2)( 0-3) | 10 |
2 | 1/3( 2-5)( 2+2)( 2-3) | 4 |
6 | 1/3( 6-5)( 6+2)( 6-3) | 8 |
Distribute (x-3)
Distribute x
Distribute 2
Subtract terms
Distribute (x-5)
Distribute x^2
Distribute - x
Distribute -6
Add and subtract terms
Distribute 1/3