1. The problem is to understand the transformation from the base function $y=x^2$ to the transformed function $y=(x-2)^2$. 2. The base function $y=x^2$ is a parabola with its vertex at the origin $(0,0)$. 3. The transformed function $y=(x-2)^2$ shifts the graph horizontally. 4. The expression $(x-2)$ inside the square means the graph moves right by 2 units because subtracting 2 inside the function shifts the graph to the right. 5. Therefore, the vertex of the parabola moves from $(0,0)$ to $(2,0)$. 6. The shape of the parabola remains the same; only its position changes. Final answer: The graph of $y=(x-2)^2$ is the graph of $y=x^2$ shifted 2 units to the right.