Precalculus Examples

$f (x) = a | x - h | + k$

Step 1

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

$x - h = 0$

Step 2

Add $h$ to both sides of the equation.

$x = h$

Step 3

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

$y = a | (h) - h | + k$

Step 4

Simplify $a | (h) - h | + k$ .

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Step 4.1

Subtract $h$ from $h$ .

$y = a | 0 | + k$

Step 4.2

Simplify each term.

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Step 4.2.1

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

$y = a \cdot 0 + k$

Step 4.2.2

Multiply $a$ by $0$ .

$y = 0 + k$

Step 4.3

Add $0$ and $k$ .

$y = k$

Step 5

The absolute value vertex is $(h, k)$ .

$(h, k)$

Step 6