Find the Vertex y=2|x-5|-4

$y = 2 | x - 5 | - 4$

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.

$y = 2 | (5) - 5 | - 4$

Step 4

Simplify $2 | (5) - 5 | - 4$ .

Simplify each term.

Subtract $5$ from $5$ .

$y = 2 | 0 | - 4$

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

$y = 2 \cdot 0 - 4$

Multiply $2$ by $0$ .

$y = 0 - 4$

Subtract $4$ from $0$ .

$y = - 4$

Step 5

The absolute value vertex is $(5, - 4)$ .

$(5, - 4)$

Step 6