Algebra: Completing a square!
Автор: SIR MORGEN ACADEMY OF MATHS & SCIENCE
Загружено: 2025-11-12
Просмотров: 23
Completing the square is an algebraic technique to rewrite a quadratic expression into the form \(a(x+h)^{2}+k\). This is done by adding and subtracting a value to make the first two terms part of a perfect square trinomial, making the expression easier to work with, particularly for solving quadratic equations or finding the vertex of a parabola. How it works Focus on the first two terms: Take the coefficient of the \(x\) term (let's call it \(b\)) and divide it by 2.Square the result: Square the value you just found \((\frac{b}{2})^{2}\).Add and subtract: Add this new value to the expression, and then immediately subtract it to keep the expression's value the same.Form the perfect square: The first three terms (\(x^{2}+bx+(\frac{b}{2})^{2}\)) can now be rewritten as a perfect square: \((x+\frac{b}{2})^{2}\).Simplify: Combine the remaining constant terms to get your final expression in the form \(a(x+h)^{2}+k\).
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