Find the Vertex f(x)=|x+5|-6

$f (x) = | x + 5 | - 6$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x + 5$ equal to $0$ . In this case, $x + 5 = 0$ .

$x + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 3

Replace the variable $x$ with $- 5$ in the expression.

$y = | (- 5) + 5 | - 6$

Step 4

Simplify $| (- 5) + 5 | - 6$ .

Simplify each term.

Add $- 5$ and $5$ .

$y = | 0 | - 6$

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

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

Step 5

The absolute value vertex is $(- 5, - 6)$ .

$(- 5, - 6)$

Step 6