Precalculus Examples

$f (x) = \frac{1}{3} | x | - 7$

Step 1

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

$x = 0$

Step 2

Replace the variable $x$ with $0$ in the expression.

$y = \frac{1}{3} \cdot | 0 | - 7$

Step 3

Simplify $\frac{1}{3} \cdot | 0 | - 7$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Remove non-negative terms from the absolute value.

$y = \frac{1}{3} \cdot 0 - 7$

Step 3.1.2

Multiply $\frac{1}{3}$ by $0$ .

$y = 0 - 7$

Step 3.2

Subtract $7$ from $0$ .

$y = - 7$

Step 4

The absolute value vertex is $(0, - 7)$ .

$(0, - 7)$

Step 5