Precalculus Examples

$y = | x + 1 | + 3$

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

$y = | (- 1) + 1 | + 3$

Simplify $| (- 1) + 1 | + 3$ .

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Simplify each term.

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Add $- 1$ and $1$ .

$y = | 0 | + 3$

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

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

The absolute value vertex is $(- 1, 3)$ .

$(- 1, 3)$

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