Chapter 2 Linear Equations and Functions - 2.7 Use Absolute Value Functions and Transformations - 2.7 Exercises - Skill Practice - Page 127: 19

$y=0.5|x+2|-1$.

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 $(-2,-1)$, $y=a|x+2|-1$. Since $(0,0)$ is on the function, plugging in the values we get: $0=a|2|-1\\0=2a-1\\1=2a\\a=0.5$. Thus $y=0.5|x+2|-1$.