Find the Vertex y=|x-3|+2

$y = | x - 3 | + 2$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 3$ equal to $0$ . In this case, $x - 3 = 0$ .

$x - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$x = 3$

Step 3

Replace the variable $x$ with $3$ in the expression.

$y = | (3) - 3 | + 2$

Step 4

Simplify $| (3) - 3 | + 2$ .

Simplify each term.

Subtract $3$ from $3$ .

$y = | 0 | + 2$

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

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

Step 5

The absolute value vertex is $(3, 2)$ .

$(3, 2)$

Step 6