1. **State the problem:** We need to find the points where the graphs of $$y = x^2 - 4x + 2$$ and $$y = -x^2 - 8x$$ intersect. 2. **Set the equations equal to find intersection points:** Since both represent $y$, set: $$x^2 - 4x + 2 = -x^2 - 8x$$ 3. **Combine like terms:** $$x^2 - 4x + 2 + x^2 + 8x = 0$$ $$2x^2 + 4x + 2 = 0$$ 4. **Simplify the equation by dividing all terms by 2:** $$x^2 + 2x + 1 = 0$$ 5. **Factor the quadratic:** $$(x + 1)^2 = 0$$ 6. **Solve for $x$:** $$x = -1$$ 7. **Find corresponding $y$ coordinate by substituting $x = -1$ into one of the original equations:** Using $$y = x^2 - 4x + 2$$: $$y = (-1)^2 - 4(-1) + 2 = 1 + 4 + 2 = 7$$ 8. **Conclusion:** The curves intersect at a single point: $$(x, y) = (-1, 7)$$