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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Pro Tip
Completing the square is how calculators and computers find roots of quadratics internally. It's also used in physics to find the time of maximum height in projectile motion (find vertex of parabola).
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Did You Know?
The quadratic formula x = (−b ± √(b²−4ac)) / 2a is derived by completing the square on the general quadratic ax²+bx+c=0. Every time you use the formula, you're implicitly completing the square.
References
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