Write an absolute value equation for the graph shown below

So, hmmm keeping in mind that, an absolute value expression is in effect a piece-wise function, let's find its "slopes", the negarive slope on the left-side and the positive slope on the right side, and let's use the vertex point as our first point

what is the slope of a line that passes through (2, -1) and (0,7)



now, what is the slope of a line that passes through (2, -1) and (4,7)



since an absolute value expression is just a piece-wise with a +/- versions, then we can just combine those two.

Hope i can you!