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Completing the square is an algebraic technique to rewrite a quadratic ax² + bx + c in the form a(x − h)² + k. It reveals the vertex of a parabola and is used to derive the quadratic formula, solve quadratic equations, and integrate rational functions.

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1. 1Start with ax² + bx + c
2. 2Factor out a from the first two terms: a(x² + (b/a)x) + c
3. 3Add and subtract (b/2a)²: a(x + b/2a)² + c − b²/4a
4. 4Result: vertex form a(x − h)² + k where h = −b/2a, k = c − b²/4a

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