1. **State the problem:** We need to find the equation of a cubic polynomial given its graph. 2. **Identify the roots:** The graph crosses the x-axis at $x = -2$, $x = 1$, and $x = 2$. These are the roots of the polynomial. 3. **Write the factored form:** Since the roots are $-2$, $1$, and $2$, the polynomial can be written as $$y = a(x + 2)(x - 1)(x - 2)$$ where $a$ is the leading coefficient. 4. **Determine the leading coefficient $a$:** The graph falls to the left (as $x \to -\infty$, $y \to -\infty$) and rises to the right (as $x \to \infty$, $y \to \infty$). This behavior indicates a negative leading coefficient for a cubic polynomial (since the end behavior is opposite to the standard positive cubic). Therefore, $a = -1$. 5. **Final equation:** Substitute $a = -1$ into the factored form: $$y = -(x + 2)(x - 1)(x - 2)$$ This is the equation of the cubic polynomial in factored form with leading coefficient $-1$.