1. **State the problem:** Identify which of the given equations matches the graph described. 2. **Analyze the graph:** The graph passes through points near $(-3,0)$ and $(1,0)$, and it touches the x-axis at $x=2$ without crossing it, indicating a repeated root at $x=2$. 3. **Recall the factor theorem:** If a polynomial has a root $r$, then $(x-r)$ is a factor. A repeated root means the factor is squared or has higher multiplicity. 4. **Check each equation's roots:** - $y = (x + 3)(x - 1)(x - 4)$ has roots at $x = -3, 1, 4$ (all simple roots). - $y = (x - 2)(x + 1)(x + 3)$ has roots at $x = 2, -1, -3$ (all simple roots). - $y = (x + 2)(x - 1)(x - 3)$ has roots at $x = -2, 1, 3$ (all simple roots). - $y = (x + 2)(x - 2)^2$ has roots at $x = -2$ (simple root) and $x = 2$ (repeated root). 5. **Match with graph behavior:** The graph touches the x-axis at $x=2$ (repeated root) and crosses at $x=-3$ and $x=1$ or near those points. The only equation with a repeated root at $x=2$ is $y = (x + 2)(x - 2)^2$. 6. **Conclusion:** The equation matching the graph is $$y = (x + 2)(x - 2)^2$$ This matches the graph's behavior of a repeated root at $x=2$ and another root at $x=-2$.