Precalculus Examples

$y = - \frac{2}{3} | x - 1 |$

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.

$y = - \frac{2}{3} \cdot | (1) - 1 |$

Step 4

Simplify $- \frac{2}{3} \cdot | (1) - 1 |$ .

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Step 4.1

Subtract $1$ from $1$ .

$y = - \frac{2}{3} \cdot | 0 |$

Step 4.2

Remove non-negative terms from the absolute value.

$y = - \frac{2}{3} \cdot 0$

Step 4.3

Multiply $- \frac{2}{3} \cdot 0$ .

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Step 4.3.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{2}{3})$

Step 4.3.2

Multiply $0$ by $\frac{2}{3}$ .

$y = 0$

Step 5

The absolute value vertex is $(1, 0)$ .

$(1, 0)$

Step 6