Find the Vertex y=|x-4|

$y = | x - 4 |$

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 4$ equal to $0$ . In this case, $x - 4 = 0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Replace the variable $x$ with $4$ in the expression.

$y = | (4) - 4 |$

Simplify $| (4) - 4 |$ .

Subtract $4$ from $4$ .

$y = | 0 |$

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 $(4, 0)$ .

$(4, 0)$