# Algebra 2 study guides

Canonical: https://duckyhelper.com/learn/algebra-2/
Updated: 2026-10-01

Each guide gives the main idea in plain words, works through examples from easy to test level, lists the mistakes students make most, and ends with five practice questions with full explanations. Every answer on these pages is recomputed by code before it is published. Work through them in order, or jump to the topic on tonight's homework.

- [Complex numbers and the imaginary unit i](https://duckyhelper.com/learn/algebra-2/complex-numbers/): How to add, subtract, multiply and divide complex numbers, simplify powers of i, and solve quadratics with complex roots. Worked examples and practice.
- [Completing the square](https://duckyhelper.com/learn/algebra-2/completing-the-square/): How to complete the square to solve quadratics, write vertex form and find a circle's center and radius. Step-by-step examples and 5 practice questions.
- [Dividing polynomials](https://duckyhelper.com/learn/algebra-2/polynomial-division/): How to divide polynomials by long division and synthetic division, and use the remainder and factor theorems. Step-by-step examples and 5 practice questions.
- [Rational expressions and equations](https://duckyhelper.com/learn/algebra-2/rational-expressions/): How to simplify, multiply, divide, add and subtract rational expressions, and solve rational equations without keeping extraneous solutions. With practice.
- [Transformations of functions](https://duckyhelper.com/learn/algebra-2/function-transformations/): How shifts, stretches and reflections change a graph, why f(x - h) moves right, and what order to apply them in. Worked examples and 5 practice questions.
- [Inverse functions](https://duckyhelper.com/learn/algebra-2/inverse-functions/): How to find the inverse of a function, check it by composition, read it on a graph, and restrict the domain when needed. Worked examples and practice.
- [Logarithms](https://duckyhelper.com/learn/algebra-2/logarithms/): What a logarithm is, the product, quotient and power rules, change of base, and how to solve exponential and log equations. Worked examples and practice.
- [Sequences and series](https://duckyhelper.com/learn/algebra-2/sequences-and-series/): Formulas for the nth term and the sum of arithmetic and geometric sequences, plus infinite geometric series, with worked examples and 5 practice questions.

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