Algebra 2

Algebra 2 Study Guide

1. Functions and Relations
      - Definition of a function
      - Domain and range
      - Function notation
      - Types of functions: linear, quadratic, polynomial, rational, exponential, logarithmic

2. Linear Functions
      - Slope-intercept form: $y = mx + b$
      - Point-slope form: $y - y_1 = m(x - x_1)$
      - Graphing linear equations
      - Systems of equations: methods of substitution and elimination

3. Quadratic Functions
      - Standard form: $y = ax^2 + bx + c$
      - Vertex form: $y = a(x - h)^2 + k$
      - Factoring quadratics
      - Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
      - Graphing parabolas: vertex, axis of symmetry, intercepts

4. Polynomials
      - Polynomial long division
      - Synthetic division
      - Finding zeros of polynomials
      - The Remainder Theorem and Factor Theorem

5. Exponential and Logarithmic Functions
      - Properties of exponents
      - Exponential growth and decay
      - Logarithmic properties: change of base, product, quotient, and power rules
      - Solving exponential and logarithmic equations

6. Rational Expressions and Equations
      - Simplifying rational expressions
      - Multiplying and dividing rational expressions
      - Adding and subtracting rational expressions
      - Solving rational equations

7. Sequences and Series
      - Arithmetic sequences: formula for the nth term
      - Geometric sequences: formula for the nth term
      - Summation notation
      - Finding sums of arithmetic and geometric series

8. Probability and Statistics
      - Measures of central tendency: mean, median, mode
      - Understanding probability: independent and dependent events
      - Combinations and permutations
      - Data representation: histograms, box plots, scatter plots

9. Conic Sections
      - Circles, ellipses, parabolas, and hyperbolas
      - Standard forms and their graphs
      - Applications of conic sections

10. Trigonometry Basics
       - Trigonometric ratios: sine, cosine, tangent
       - Inverse trigonometric functions
       - Unit circle and angle measures
       - Solving right triangles
       - Graphing trigonometric functions