Precalculus Examples

$y = 5 - | x - 1 |$

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.

$y = 5 - | (1) - 1 |$

Step 4

Simplify $5 - | (1) - 1 |$ .

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

Subtract $1$ from $1$ .

$y = 5 - | 0 |$

Step 4.1.2

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

$y = 5 - 0$

Step 4.1.3

Multiply $- 1$ by $0$ .

$y = 5 + 0$

Step 4.2

Add $5$ and $0$ .

$y = 5$

Step 5

The absolute value vertex is $(1, 5)$ .

$(1, 5)$

Step 6