Find the Vertex f(x)=|x+1|-7

$f (x) = | x + 1 | - 7$

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

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

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

$y = | (- 1) + 1 | - 7$

Step 4

Simplify $| (- 1) + 1 | - 7$ .

Simplify each term.

Add $- 1$ and $1$ .

$y = | 0 | - 7$

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

$y = 0 - 7$

Subtract $7$ from $0$ .

$y = - 7$

Step 5

The absolute value vertex is $(- 1, - 7)$ .

$(- 1, - 7)$

Step 6