Public learning track
Advanced Quadratics, Discriminant Analysis, and Inequalities
12th Grade · Math · Open Global Math
7 lessons
Goal
Analyze quadratic functions in depth, evaluate discriminants across real and complex roots, and solve quadratic and linear inequalities in one and two variables.
Featured Diagrams
Completing the Square with Arbitrary Leading Coefficients
7 lessons
0 of 7 done
- 1Completing the Square with Arbitrary Leading CoefficientsUp nextStart
- 2Evaluating the Discriminant for Real, Repeated, and Complex RootsPremiumNot started yet
- 3Solving Quadratic Equations with Complex SolutionsNot started yet
- 4Solving One-Variable Quadratic Inequalities AlgebraicallyNot started yet
- 5Expressing Inequality Solutions in Interval and Set NotationNot started yet
- 6Graphing Linear and Quadratic Inequalities in Two VariablesNot started yet
- 7Modeling and Optimizing Real-World Scenarios with Quadratic InequalitiesNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
7 lessons
Advanced Quadratics, Discriminant Analysis, and Inequalities
Analyze quadratic functions in depth, evaluate discriminants across real and complex roots, and solve quadratic and linear inequalities in one and two variables.
2
6 lessons
Non-Linear Systems and Geometric Intersections
Solve simultaneous linear and nonlinear systems algebraically and interpret solutions as intersection points or tangencies of curves.
3
8 lessons
Formal Functions, Composition, and Inverses
Define formal function mappings, evaluate and decompose composite functions, and construct inverse functions with domain restrictions.
4
7 lessons
Polynomial, Modulus, and Piecewise Function Analysis
Analyze key features, symmetry, extrema, end behavior, and graphs of polynomial, modulus, and piecewise functions.
5
6 lessons
Rational and Power Functions: Asymptotes and Behavior
Analyze power and rational functions, finding vertical, horizontal, and oblique asymptotes, removable singularities, and global behavior.
6
7 lessons
General Function Transformations
Apply and analyze combined vertical and horizontal translations, reflections, stretches, and compressions in the form y = a f(b(x - h)) + k.
7
7 lessons
Limits, Continuity, and Discontinuities
Investigate function continuity, analyze one-sided limits, classify removable, jump, and infinite discontinuities, and evaluate graphing technology limitations.