Algebra Examples

$f (x) = \frac{1}{2} | x + 1 | - \frac{3}{7}$

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

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

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

$y = \frac{1}{2} \cdot | (- 1) + 1 | - \frac{3}{7}$

Step 4

Simplify $\frac{1}{2} \cdot | (- 1) + 1 | - \frac{3}{7}$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Add $- 1$ and $1$ .

$y = \frac{1}{2} \cdot | 0 | - \frac{3}{7}$

Step 4.1.2

Remove non-negative terms from the absolute value.

$y = \frac{1}{2} \cdot 0 - \frac{3}{7}$

Step 4.1.3

Multiply $\frac{1}{2}$ by $0$ .

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

Step 4.2

Subtract $\frac{3}{7}$ from $0$ .

$y = - \frac{3}{7}$

Step 5

The absolute value vertex is $(- 1, - \frac{3}{7})$ .

$(- 1, - \frac{3}{7})$

Step 6