Question

Which absolute value function defines this graph?

Answer 1

The vertex of the graph is at (-2, 3).

This means the equation is of the form $f(x)=a|x+2|+3$.

Substituting in the coordinates of one of the other points on the graph that is not the vertex, such as (-1, -1),

$-1=a|-1+2|+3\\\\-1=a+3\\\\a=-4$

So, the equation is $\boxed{f(x)=-4|x+2|+3}$