Precalculus Examples

$| x + 2 | = y$

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$y = | x + 2 |$

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x + 2$ equal to $0$ . In this case, $x + 2 = 0$ .

$x + 2 = 0$

Since $2$ does not contain the variable to solve for, move it to the right side of the equation by subtracting $2$ from both sides.

$x = - 2$

Replace the variable $x$ with $- 2$ in the expression.

$y = | (- 2) + 2 |$

Simplify $| (- 2) + 2 |$ to get $0$ .

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Add $- 2$ and $2$ to get $0$ .

$y = | 0 |$

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

$y = 0$

The absolute value vertex is $(- 2, 0)$ .

$(- 2, 0)$

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