High school · Math
Algebra 2
Algebra 2 extends equation-solving and functions to more complex patterns, including exponential and logarithmic relationships.
What you will learn
- Analyze polynomial and rational functions.
- Solve quadratic equations in several ways.
- Work with radicals and complex numbers.
- Connect exponential functions and logarithms.
- Model patterns with functions and sequences.
Common challenges
Keeping track of restrictions
Denominators cannot equal zero, and real square roots need nonnegative inputs. Write restrictions before simplifying.
Choosing a method
A quadratic may be easier to factor, complete the square, or solve with the formula. Look at its structure before starting.
Extra solutions
Squaring both sides can introduce answers that do not fit the original equation. Substitute every candidate back into the original.
Key concepts
- Function families
- Linear, quadratic, exponential, and other families have recognizable rules and graph shapes.
- Complex numbers
- The number i satisfies i^2 = -1. Complex numbers have the form a + bi.
- Polynomial zeros
- Zeros are inputs that make a polynomial equal zero. Factoring can reveal these inputs.
- Rational expressions
- These are ratios of polynomials. Simplifying them does not remove restrictions from the original denominator.
- Logarithms
- A logarithm answers an exponent question. For example, log base 2 of 8 is 3 because 2^3 = 8.
- Inverse functions
- Inverse functions undo each other on suitable domains. Their inputs and outputs switch roles.
How to prepare
- Review solving and graphing linear equations.
- Practice factoring simple quadratics.
- Review exponent rules with numerical examples.
- Practice fractions with variables and note excluded values.
Study habits that help
- Compare graph shapes for different function families.
- Keep an example of each quadratic-solving method.
- Write domain restrictions before canceling factors.
- Check radical-equation answers in the original equation.
What to expect
- Typical workload
- Moderate
- Time outside class
- Typically about 3 to 6 hours outside class; this varies by school and topic.
- Pace
- New function families often arrive quickly and reuse earlier algebra skills.
- How it is usually graded
- Tests, quizzes, homework, and sometimes modeling projects typically determine grades.
Skills that help
- Factoring
- Fraction operations
- Graph interpretation
- Multi-step organization
What teachers usually expect
- State restrictions when needed.
- Show algebraic steps even when using technology.
- Review earlier methods throughout the year.
Before you start
- Typical Algebra 1 fluency
- Graphing and solving linear systems
- Basic geometry and square-root skills are often helpful
These are general descriptions of a typical course. Workload, pace and prerequisites differ by school and instructor, so check with your counselor, advisor or the course catalog.
Where it can lead
- Engineering
- Economics
- Computer science
- Natural sciences
Flashcards
Card 1 of 10
Practice questions
Question 1 of 6
Solve x^2 - 5x + 6 = 0.
Vocabulary
- Polynomial
- A sum of terms with nonnegative integer powers of variables.
- Degree
- The highest exponent with a nonzero coefficient in a one-variable polynomial.
- Radical
- An expression involving a root, such as a square root.
- Asymptote
- A line a graph approaches in a specified limiting direction.
- Exponential function
- A function with the variable in an exponent, such as 2^x.
- Logarithm
- The exponent needed to produce a given positive number from a given base.
- Composition
- Using one function's output as another function's input.
- Sequence
- An ordered list of terms following an indexing rule.