Precalculus Examples

$f (x) = | x - 4 | + 3$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 4$ equal to $0$ . In this case, $x - 4 = 0$ .

$x - 4 = 0$

Step 2

Add $4$ to both sides of the equation.

$x = 4$

Step 3

Replace the variable $x$ with $4$ in the expression.

$y = | (4) - 4 | + 3$

Step 4

Simplify $| (4) - 4 | + 3$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Subtract $4$ from $4$ .

$y = | 0 | + 3$

Step 4.1.2

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

$y = 0 + 3$

Step 4.2

Add $0$ and $3$ .

$y = 3$

Step 5

The absolute value vertex is $(4, 3)$ .

$(4, 3)$

Step 6