Find the Vertex f(x)=|x-13|+11

$f (x) = | x - 13 | + 11$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 13$ equal to $0$ . In this case, $x - 13 = 0$ .

$x - 13 = 0$

Step 2

Add $13$ to both sides of the equation.

$x = 13$

Step 3

Replace the variable $x$ with $13$ in the expression.

$y = | (13) - 13 | + 11$

Step 4

Simplify $| (13) - 13 | + 11$ .

Simplify each term.

Subtract $13$ from $13$ .

$y = | 0 | + 11$

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

$y = 0 + 11$

Add $0$ and $11$ .

$y = 11$

Step 5

The absolute value vertex is $(13, 11)$ .

$(13, 11)$

Step 6