Algebra Examples

$f (x) = | x + 8 | - 3$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x + 8$ equal to $0$ . In this case, $x + 8 = 0$ .

$x + 8 = 0$

Step 2

Subtract $8$ from both sides of the equation.

$x = - 8$

Step 3

Replace the variable $x$ with $- 8$ in the expression.

$y = | (- 8) + 8 | - 3$

Step 4

Simplify $| (- 8) + 8 | - 3$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Add $- 8$ and $8$ .

$y = | 0 | - 3$

Step 4.1.2

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

$y = 0 - 3$

Step 4.2

Subtract $3$ from $0$ .

$y = - 3$

Step 5

The absolute value vertex is $(- 8, - 3)$ .

$(- 8, - 3)$

Step 6