Shifting a V

The shift rules belong to the brackets, not to the parabola, so they work for any function. Let $f\left(x\right) = \left|x\right|$ this time. Its graph is a V with its corner at (0, 0), and each arm rises 1 for every step sideways, through (1, 1) and (-1, 1).

Take $y = f\left(x-3\right)+1$. Inside, $x-3$ is 0 when x is 3, so the V moves 3 right. Outside, the plus 1 lifts it 1. The corner lands at (3, 1), and the arms still rise 1 per step, through (4, 2) and (2, 2).

The dashed parent V, and the same V with its corner at (3, 1).

For a V, the vertex is the corner. Place the corner first, then one point on an arm, and the whole graph is fixed.