Find the Vertex f(x)=1/2|x|-4/5

$f (x) = \frac{1}{2} | x | - \frac{4}{5}$

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.

$y = \frac{1}{2} \cdot | 0 | - \frac{4}{5}$

Step 3

Simplify $\frac{1}{2} \cdot | 0 | - \frac{4}{5}$ .

Simplify each term.

Remove non-negative terms from the absolute value.

$y = \frac{1}{2} \cdot 0 - \frac{4}{5}$

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

$y = 0 - \frac{4}{5}$

Subtract $\frac{4}{5}$ from $0$ .

$y = - \frac{4}{5}$

Step 4

The absolute value vertex is $(0, - \frac{4}{5})$ .

$(0, - \frac{4}{5})$

Step 5