Precalculus Examples

$Y = | x - 1 | + 3$

Step 1

Rewrite the equation in terms of $x$ and $y$ .

$y = | x - 1 | + 3$

Step 2

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 3

Add $1$ to both sides of the equation.

$x = 1$

Step 4

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

$y = | (1) - 1 | + 3$

Step 5

Simplify $| (1) - 1 | + 3$ .

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Step 5.1

Simplify each term.

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Step 5.1.1

Subtract $1$ from $1$ .

$y = | 0 | + 3$

Step 5.1.2

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

$y = 0 + 3$

Step 5.2

Add $0$ and $3$ .

$y = 3$

Step 6

The absolute value vertex is $(1, 3)$ .

$(1, 3)$

Step 7