Find the Vertex y=|x-1|+8

$y = | x - 1 | + 8$

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

Add $1$ to both sides of the equation.

$x = 1$

Step 3

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

$y = | (1) - 1 | + 8$

Step 4

Simplify $| (1) - 1 | + 8$ .

Simplify each term.

Subtract $1$ from $1$ .

$y = | 0 | + 8$

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

$y = 0 + 8$

Add $0$ and $8$ .

$y = 8$

Step 5

The absolute value vertex is $(1, 8)$ .

$(1, 8)$

Step 6