Find the Vertex f(x)=|x-5|+10

$f (x) = | x - 5 | + 10$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 5$ equal to $0$ . In this case, $x - 5 = 0$ .

$x - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$x = 5$

Step 3

Replace the variable $x$ with $5$ in the expression.

$y = | (5) - 5 | + 10$

Step 4

Simplify $| (5) - 5 | + 10$ .

Simplify each term.

Subtract $5$ from $5$ .

$y = | 0 | + 10$

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

$y = 0 + 10$

Add $0$ and $10$ .

$y = 10$

Step 5

The absolute value vertex is $(5, 10)$ .

$(5, 10)$

Step 6