Public learning track
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.
Featured Diagrams
Using the Discriminant to Determine the Nature of Roots
6 lessons
0 of 6 done
- 1Using the Discriminant to Determine the Nature of RootsUp nextStart
- 2Finding Parameter Ranges Using the DiscriminantPremiumNot started yet
- 3Completing the Square for General Quadratic ExpressionsNot started yet
- 4Optimizing Quadratic Objective FunctionsNot started yet
- 5Solving Equations in Quadratic Form by SubstitutionNot started yet
- 6Solving Trigonometric and Exponential Equations in Quadratic FormNot started yet
Curriculum Framework
11th Grade · Math · Open Global Math
1
9 lessons
Polynomial Theorems, Division, and Advanced Factoring
Master polynomial operations, algebraic long division, the Remainder and Factor Theorems, and factoring techniques for higher-degree polynomials.
2
5 lessons
Rational Expressions and Algebraic Fractions
Simplify, add, subtract, multiply, and divide complex rational expressions and simplify compound algebraic fractions.
3
6 lessons
Partial Fraction Decomposition
Decompose proper and improper rational expressions into partial fractions with distinct linear, repeated linear, and irreducible quadratic denominators.
4
6 lessons
Advanced Quadratic Forms, Discriminant, and Optimization
Analyze quadratic forms using discriminant analysis, solve equations reducible to quadratics, and optimize objective functions via completing the square.
5
6 lessons
Simultaneous Equations and Nonlinear Systems
Solve simultaneous linear and nonlinear systems in two variables algebraically and interpret solutions geometrically.
6
6 lessons
Linear and Quadratic Inequalities
Solve single-variable linear and quadratic inequalities, graph two-variable inequality regions, and express solution sets using interval and set notation.
7
5 lessons
Binomial Theorem with Positive Integers
Expand binomial expressions with positive integer powers using Pascal's triangle, combinatorics, and sigma notation.
8
6 lessons
General Binomial Series and Rational Exponents
Expand (1 + x)ⁿ and (a + bx)ⁿ for any rational exponent n, determine radius of convergence, and perform numerical approximations.