Completing the Square for General Quadratic Expressions

Advanced Quadratic Forms, Discriminant, and Optimization

11th Grade·Math·Open Global Math

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Transform general quadratic forms ax² + bx + c into vertex form a(x + p)² + q with non-unitary leading coefficients.

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Advanced Quadratic Forms, Discriminant, and Optimization

11th Grade · Math · Open Global Math

6 lessons

Goal

Analyze quadratic forms using discriminant analysis, solve equations reducible to quadratics, and optimize objective functions via completing the square.

6 lessons

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Using the Discriminant to Determine the Nature of RootsUp next
Finding Parameter Ranges Using the DiscriminantNot started yet
Completing the Square for General Quadratic ExpressionsYou are here
Optimizing Quadratic Objective FunctionsNot started yet
Solving Equations in Quadratic Form by SubstitutionNot started yet
Solving Trigonometric and Exponential Equations in Quadratic FormNot started yet

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Learning standards covered

OGM.12.ALG.3Open Global Math Standards 2026™ · 11th Grade

Solve quadratic equations in a function of the unknown, utilize the discriminant to determine root nature, and complete the square to analyze quadratic forms and optimize objective functions.