1. **State the problem:** Find the points of intersection of the two parabolas given by the equations: $$y = x^2 - 2x + 2$$ $$y = x^2 - 8x + 20$$ 2. **Set the equations equal to find intersection points:** At points of intersection, the $y$ values are equal, so: $$x^2 - 2x + 2 = x^2 - 8x + 20$$ 3. **Simplify the equation:** Subtract $x^2$ from both sides: $$\cancel{x^2} - 2x + 2 = \cancel{x^2} - 8x + 20$$ which simplifies to: $$-2x + 2 = -8x + 20$$ 4. **Solve for $x$:** Add $8x$ to both sides: $$-2x + 8x + 2 = 20$$ which is: $$6x + 2 = 20$$ Subtract 2 from both sides: $$6x = 18$$ Divide both sides by 6: $$x = \frac{18}{6}$$ $$x = 3$$ 5. **Find corresponding $y$ value:** Substitute $x=3$ into either original equation, for example: $$y = 3^2 - 2(3) + 2 = 9 - 6 + 2 = 5$$ 6. **Conclusion:** The two parabolas intersect at the point: $$(3, 5)$$