Yes, and it has a coordinate geometry interpretation too. Completing the square represents the original quadratic function as a basic x^2 parabola that's been s

Yes, and it has a coordinate geometry interpretation too. Completing the square represents the original quadratic function as a basic x^2 parabola that's been scaled vertically, shifted vertically, then shifted horizontally. If you understand what each of these three operations do to the roots of the parabola, you can derive the quadratic formula. (It's basically just the algebraic way with diagrams, but may help the geometry-loving/algebra-hating types out there.)