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Algebra Examples Absolute Value Expressions and Equations

Find the Vertex

$y = | x - 1 |$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 1$ equal to $0$ . In this case, $x - 1 = 0$ .

$x - 1 = 0$

Step 2

Add $1$ to both sides of the equation.

$x = 1$

Step 3

Replace the variable $x$ with $1$ in the expression.

$y = | (1) - 1 |$

Step 4

Simplify $| (1) - 1 |$ .

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Step 4.1

Subtract $1$ from $1$ .

$y = | 0 |$

Step 4.2

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$y = 0$

Step 5

The absolute value vertex is $(1, 0)$ .

$(1, 0)$

Step 6

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Absolute Value Expressions and Equations

More step-by-step Algebra examples from this chapter.

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$