Chapter 2 Linear Equations and Functions - 2.7 Use Absolute Value Functions and Transformations - 2.7 Exercises - Skill Practice - Page 127: 20

$y=2|x-5|+2$.

The absolute value functions have the form $y=a|x-b|+c$ where $(b,c)$ is the vertex of the function. Hence here because the vertex is at $(5,2)$, $y=a|x-5|+2$. Since $(4,4)$ is on the function, plugging in the values we get: $4=a|4-5|+2\\2=a$. Thus $y=2|x-5|+2$.