1. The problem states that the black graph is $y = f(x)$, a parabola with vertex at $(0,0)$. 2. The red graph is a horizontal translation of the black graph 3 units to the left, with vertex at $(-3,0)$. 3. Horizontal translations of a function $f(x)$ are given by $y = f(x - h)$, where $h$ is the horizontal shift. 4. A shift 3 units to the left means $h = -3$, so the function becomes $y = f(x - (-3)) = f(x + 3)$. 5. Therefore, the equation for the red graph is $y = f(x + 3)$. 6. The other options involve vertical shifts or incorrect horizontal shifts. Final answer: $y = f(x + 3)$