Solving Equations in Quadratic Form by Substitution

Advanced Quadratic Forms, Discriminant, and Optimization

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Solve equations reducible to quadratic form using substitution u = f(x) for polynomial, rational, exponential, and radical expressions.

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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

0 of 6 done

Using the Discriminant to Determine the Nature of RootsUp next
Finding Parameter Ranges Using the DiscriminantNot started yet
Completing the Square for General Quadratic ExpressionsNot started yet
Optimizing Quadratic Objective FunctionsNot started yet
Solving Equations in Quadratic Form by SubstitutionYou are here
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.