Precalculus Examples

Graph f(x)=-x(x-2)(x+2)
Step 1
Find the point at .
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Step 1.1
Replace the variable with in the expression.
Step 1.2
Simplify the result.
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Step 1.2.1
Simplify each term.
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Step 1.2.1.1
Raise to the power of .
Step 1.2.1.2
Multiply by .
Step 1.2.1.3
Multiply by .
Step 1.2.2
Subtract from .
Step 1.2.3
The final answer is .
Step 1.3
Convert to decimal.
Step 2
Find the point at .
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Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Multiply by by adding the exponents.
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Step 2.2.1.1.1
Multiply by .
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Step 2.2.1.1.1.1
Raise to the power of .
Step 2.2.1.1.1.2
Use the power rule to combine exponents.
Step 2.2.1.1.2
Add and .
Step 2.2.1.2
Raise to the power of .
Step 2.2.1.3
Multiply by .
Step 2.2.2
Subtract from .
Step 2.2.3
The final answer is .
Step 2.3
Convert to decimal.
Step 3
Find the point at .
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Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
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Step 3.2.1
Simplify each term.
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Step 3.2.1.1
Raising to any positive power yields .
Step 3.2.1.2
Multiply by .
Step 3.2.1.3
Multiply by .
Step 3.2.2
Add and .
Step 3.2.3
The final answer is .
Step 3.3
Convert to decimal.
Step 4
Find the point at .
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Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
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Step 4.2.1
Simplify each term.
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Step 4.2.1.1
One to any power is one.
Step 4.2.1.2
Multiply by .
Step 4.2.1.3
Multiply by .
Step 4.2.2
Add and .
Step 4.2.3
The final answer is .
Step 4.3
Convert to decimal.
Step 5
Find the point at .
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Step 5.1
Replace the variable with in the expression.
Step 5.2
Simplify the result.
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Step 5.2.1
Simplify each term.
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Step 5.2.1.1
Raise to the power of .
Step 5.2.1.2
Multiply by .
Step 5.2.1.3
Multiply by .
Step 5.2.2
Add and .
Step 5.2.3
The final answer is .
Step 5.3
Convert to decimal.
Step 6
The cubic function can be graphed using the function behavior and the points.
Step 7
The cubic function can be graphed using the function behavior and the selected points.
Rises to the left and falls to the right
Step 8