1. The problem asks to translate the graph of $y = x^2$ to get the graph of $y = x^2 - 2$. 2. The formula for vertical translation of a function $f(x)$ is $f(x) + k$, where $k$ is the number of units moved up (if $k > 0$) or down (if $k < 0$). 3. Here, $y = x^2 - 2$ means the graph of $y = x^2$ is translated down by 2 units. 4. This shifts every point on the parabola down by 2, moving the vertex from $(0,0)$ to $(0,-2)$. 5. Therefore, the graph of $y = x^2 - 2$ is the parabola $y = x^2$ shifted down 2 units.