Chapter 2 Linear Equations and Functions - 2.8 Graph Linear Inequalities in Two Variables - 2.8 Exercises - Quiz for Lessons 2.7-2.8 - Page 138: 4

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

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 $(0,-2)$, $y=a|x|-2$. Since $(-1,-4)$ is on the function, plugging in the values we get: $-4=a|-1|-2\\-4=a-2\\\\-2=a$. Thus $y=-2|x|-2$.