Find the Vertex y=|x-2|+1

$y = | x - 2 | + 1$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 2$ equal to $0$ . In this case, $x - 2 = 0$ .

$x - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

$x = 2$

Step 3

Replace the variable $x$ with $2$ in the expression.

$y = | (2) - 2 | + 1$

Step 4

Simplify $| (2) - 2 | + 1$ .

Simplify each term.

Subtract $2$ from $2$ .

$y = | 0 | + 1$

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

$y = 0 + 1$

Add $0$ and $1$ .

$y = 1$

Step 5

The absolute value vertex is $(2, 1)$ .

$(2, 1)$

Step 6