Precalculus Examples

Step 1
To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .
Step 2
Solve the equation to find the coordinate for the absolute value vertex.
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Step 2.1
Combine and .
Step 2.2
Subtract from both sides of the equation.
Step 2.3
Multiply both sides of the equation by .
Step 2.4
Simplify both sides of the equation.
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Step 2.4.1
Simplify the left side.
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Step 2.4.1.1
Cancel the common factor of .
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Step 2.4.1.1.1
Cancel the common factor.
Step 2.4.1.1.2
Rewrite the expression.
Step 2.4.2
Simplify the right side.
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Step 2.4.2.1
Multiply by .
Step 3
Replace the variable with in the expression.
Step 4
Simplify .
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Step 4.1
Cancel the common factor of .
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Step 4.1.1
Factor out of .
Step 4.1.2
Cancel the common factor.
Step 4.1.3
Rewrite the expression.
Step 4.2
Add and .
Step 4.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 5
The absolute value vertex is .
Step 6
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