CurriculumGrade 11Mathematics

Rewriting Expressions (Completing the Square)

Aligned to A-SSE.B.3 — Common Core State Standards for Mathematics.

What this lesson teaches

Equivalent forms of an expression reveal different information. Completing the square rewrites a quadratic to expose its vertex (maximum or minimum).

Worked example

x² + 6x + 5 = (x+3)² − 4. The vertex form shows a minimum at (−3, −4).

Practice questions

  1. Complete the square for x² + 4x.
  2. What does vertex form tell you that standard form hides?
  3. Rewrite x² + 8x + 10 in vertex form.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Reescritura de Expresiones (Completar el Cuadrado)

Las formas equivalentes de una expresión revelan información diferente. Completar el cuadrado reescribe una expresión cuadrática para mostrar su vértice (máximo o mínimo).

Ejemplo: x² + 6x + 5 = (x+3)² − 4. La forma de vértice muestra un mínimo en (−3, −4).

More Algebra lessons

Zeros and Factors of PolynomialsA-APR.B.3Sum of a Finite Geometric SeriesA-SSE.B.4The Remainder TheoremA-APR.B.2Proving Polynomial IdentitiesA-APR.C.4Rewriting Rational ExpressionsA-APR.D.6Creating Equations to Model ProblemsA-CED.A.1

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