Algebra

Master essential algebraic concepts in this comprehensive 7-hour course covering exponent rules, radicals, factoring, rational expressions, quadratic equations, inequalities, coordinate geometry, functions, polynomials, exponential and logarithmic functions, and systems of equations. Learn to simplify expressions, solve various equation types, graph functions, apply transformations, interpret real-world applications, and manipulate complex mathematical concepts through a wide range of topics from basic algebra to advanced function analysis.

Exponent Rules.
Simplifying using Exponent Rules.
Simplifying Radicals.
Simplifying Radicals, Snow Day Examples.
Factoring.
Factoring - Additional Examples.
Rational Expressions.
Solving Quadratic Equations.
Solving Rational Equations.
Solving Radical Equations.
Absolute Value Equations.
Interval Notation.
Absolute Value Inequalities.
Compound Linear Inequalities.
Polynomial and Rational Inequalities.
Distance Formula.
Midpoint Formula.
Circles: Graphs and Equations.
Lines: Graphs and Equations.
Parallel and Perpendicular Lines.
Functions.
Toolkit Functions.
Transformations of Functions.
Introduction to Quadratic Functions.
Graphing Quadratic Functions.
Standard Form and Vertex Form for Quadratic Functions.
Justification of the Vertex Formula.
Polynomials.
Exponential Functions.
Exponential Function Applications.
Exponential Functions Interpretations.
Compound Interest.
Logarithms: Introduction.
Log Functions and Their Graphs.
Combining Logs and Exponents.
Log Rules.
Solving Exponential Equations Using Logs.
Solving Log Equations.
Doubling Time and Half Life.
Systems of Linear Equations.
Distance, Rate, and Time Problems.
Mixture Problems.
Rational Functions and Graphs.
Combining Functions.
Composition of Functions.
Inverse Functions.