The parent function of absolute value is f(x)=|x| and looks like
the graph below. Note the vertex is at (0,0) and the slope of the left branch of the graph is −1 while the slope of the right branch is +1.
graph{abs(x) [-10, 10, -5, 5]}
Given the form, f(x)=m|x−h|+k,
±m represents the slope of each branch of the graph. A positive value of m in the original equation means the graph has a "V" shape, while a negative value of m means the graph has an "upside-down V-shape".
(h,k) is the vertex. The vertex is shifted horizontally by h units and vertically by k units.
f(x)=2|x−1|−3
In this example, m=2 is positive, and the graph will have a V-shape. The left branch of the V has a slope of −2 and the right branch has a slope of 2.
The vertex is (1,−3), which represents a shift of one unit to the right and 3 units down.
graph{2abs(x-1)-3 [-10, 10, -5, 5]}
