Analyze \(y~=~|x~-~3|~+~2\). State \(a\), \(h\), and \(k\); give the vertex, opening, left and right arm slopes, and range; and list symmetric anchors \(\text{one}\) and \(\text{two}~\text{units}\) from the vertex.

Treat the absolute-value equation as vertex form first: the horizontal and vertical shifts locate the corner before any other points are plotted. Then use the coefficient’s sign to set the opening and its magnitude to set the arm slopes. A pair of symmetric anchor points is a quick check that the whole V has been transformed consistently.