Find the Vertex f(x)=3/5|x-5|+2/3

$f (x) = \frac{3}{5} | x - 5 | + \frac{2}{3}$

Step 1

To find the $x$ coordinate of the vertex, set the inside of the absolute value $x - 5$ equal to $0$ . In this case, $x - 5 = 0$ .

$x - 5 = 0$

Step 2

Add $5$ to both sides of the equation.

$x = 5$

Step 3

Replace the variable $x$ with $5$ in the expression.

$y = \frac{3}{5} \cdot | (5) - 5 | + \frac{2}{3}$

Step 4

Simplify $\frac{3}{5} \cdot | (5) - 5 | + \frac{2}{3}$ .

Simplify each term.

Subtract $5$ from $5$ .

$y = \frac{3}{5} \cdot | 0 | + \frac{2}{3}$

Remove non-negative terms from the absolute value.

$y = \frac{3}{5} \cdot 0 + \frac{2}{3}$

Multiply $\frac{3}{5}$ by $0$ .

$y = 0 + \frac{2}{3}$

Add $0$ and $\frac{2}{3}$ .

$y = \frac{2}{3}$

Step 5

The absolute value vertex is $(5, \frac{2}{3})$ .

$(5, \frac{2}{3})$

Step 6