1. **State the problem:** Solve the quadratic equation $$x^2 + x - 6 = 0$$ using the graph of the function $$y = x^2 + x - 6$$. 2. **Formula and rules:** The solutions to $$x^2 + x - 6 = 0$$ are the x-values where the graph of $$y = x^2 + x - 6$$ intersects the x-axis (i.e., where $$y=0$$). 3. **Factor the quadratic:** $$x^2 + x - 6 = (x + 3)(x - 2)$$ 4. **Set each factor equal to zero:** $$x + 3 = 0 \Rightarrow x = -3$$ $$x - 2 = 0 \Rightarrow x = 2$$ 5. **Interpretation:** The graph crosses the x-axis at $$x = -3$$ and $$x = 2$$, so these are the solutions to the equation. 6. **Verify by substitution:** For $$x = -3$$: $$(-3)^2 + (-3) - 6 = 9 - 3 - 6 = 0$$ For $$x = 2$$: $$2^2 + 2 - 6 = 4 + 2 - 6 = 0$$ **Final answer:** $$x = -3$$ and $$x = 2$$