1. The problem asks how the graph of the quadratic function $y = (x - 3)^2$ moves compared to the parent function $y = x^2$. 2. The general form for a horizontal shift of a quadratic function is $y = (x - h)^2$, where $h$ is the horizontal shift. 3. If $h$ is positive, the graph shifts to the right by $h$ units; if $h$ is negative, it shifts to the left by $|h|$ units. 4. In this case, $h = 3$, so the graph shifts 3 units to the right. 5. The graph does not move up or down because there is no vertical shift term added or subtracted outside the squared expression. 6. Therefore, the graph of $y = (x - 3)^2$ moves to the RIGHT 3 units compared to $y = x^2$. Final answer: The graph moves to the RIGHT 3 units.