# Algebra Examples

To find the coordinate of the vertex, set the inside of the absolute value equal to . In this case, .
Solve the equation to find the coordinate for the absolute value vertex.
Rewrite as a set of linear factors.
Divide each term by and simplify.
Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
Multiply by to get .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by to get .
Divide by to get .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Replace the variable with in the expression.
Simplify to get .
Simplify each term.
Remove parentheses around .
Raising to any positive power yields .
Multiply by to get .
The absolute value is the distance between a number and zero. The distance between and is .
Multiply by to get .
The absolute value vertex is .

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