Level up your algebra skills, learn about functions and graphing, and dive deep into quadratics.

- Create equations that describe relationships between quantities.
- Relate the solutions of two-variable equations and inequalities to graphs in the coordinate plane.
- Set up and solve systems of linear equations in real-world modeling contexts.

- Leverage multiplication as a strategy to transform rational equations into linear equations.
- Extend prior knowledge of radicals and solving linear equations to handle cases when the variable is raised to a power.
- Relate absolute value to distance on the number line and apply this understanding to solve absolute value equations and inequalities.

- Leverage the distributive property and an understanding of like terms to manipulate polynomial expressions.
- Understand the relationship between multiplication and factoring and apply a systematic method to factor trinomials with leading coefficients.
- Leverage factoring and the quadratic formula as complementary techniques for solving quadratic equations and graphing quadratic functions.

- Identify, interpret, and build functions that model relationships between two quantities.
- Represent and reason about functions and sequences using formal notation.

- Visualize functions in the coordinate plane by graphing.
- Leverage the coordinate plane as a tool to represent and solve problems involving geometry and data.
- Understand how transformations affect the shape of a function's graph and use this understanding to graph transformed absolute value functions.

1.

Equations & Inequalities
23 topics

1.1. Linear Equations

1.1.1. | Solving Linear Equations With Unknown Coefficients | |

1.1.2. | Solving Linear Equations With Unknown Coefficients by Factoring | |

1.1.3. | Solving Linear Inequalities With Unknown Parameters | |

1.1.4. | Solving Many-Variable Equations |

1.2. Modeling With Linear Equations

1.2.1. | Interpreting Linear Expressions | |

1.2.2. | Modeling With Linear Equations | |

1.2.3. | Consecutive Integer Problems | |

1.2.4. | Speed, Distance, Time Problems | |

1.2.5. | Further Speed, Distance, Time Problems | |

1.2.6. | Modeling Work Problems | |

1.2.7. | Modeling Mixture Problems |

1.3. Linear Inequalities

1.3.1. | Solving Compound Inequalities | |

1.3.2. | Expressing Inequalities Using Interval Notation | |

1.3.3. | Unions of Intervals | |

1.3.4. | Intersections of Intervals | |

1.3.5. | Compound OR Inequalities | |

1.3.6. | Compound AND Inequalities | |

1.3.7. | Introduction to Modeling With Inequalities | |

1.3.8. | Modeling With One-Step Inequalities | |

1.3.9. | Modeling With Two-Step Inequalities |

1.4. Nonlinear Equations

1.4.1. | Solving Equations Using the Square Root Method | |

1.4.2. | Solving Equations With Odd Exponents Using the Nth Root Method | |

1.4.3. | Solving Equations With Even Exponents Using the Nth Root Method |

2.

Two-Variable Equations & Inequalities
22 topics

2.5. Graphs of Linear Equations

2.5.1. | Equations of Lines in Slope-Intercept Form | |

2.5.2. | Finding Properties of Lines Given in Slope-Intercept Form | |

2.5.3. | Equations of Lines in Point-Slope Form | |

2.5.4. | Equations of Lines in Standard Form | |

2.5.5. | Determining Properties of Lines Given in Standard Form |

2.6. Modeling With Two-Variable Linear Equations

2.6.1. | Modeling With Linear Equations in Two Variables | |

2.6.2. | Further Modeling With Linear Equations in Two Variables | |

2.6.3. | Analyzing and Interpreting Graphs of Linear Equations | |

2.6.4. | Distance-Time Graphs | |

2.6.5. | Calculating Acceleration From a Speed-Time Graph | |

2.6.6. | Calculating Distance From a Speed-Time Graph |

2.7. Systems of Equations

2.7.1. | Systems of Linear Equations With Fractional Coefficients | |

2.7.2. | Systems of Linear Equations With Decimal Coefficients | |

2.7.3. | Modeling Number Problems Using Systems of Linear Equations | |

2.7.4. | Modeling Coin Problems Using Systems of Linear Equations | |

2.7.5. | Solving Systems of Nonlinear Equations Using Graphs | |

2.7.6. | Approximating Solutions to Systems of Nonlinear Equations |

2.8. Two-Variable Linear Inequalities

2.8.1. | Graphing Strict Two-Variable Linear Inequalities | |

2.8.2. | Graphing Non-Strict Two-Variable Linear Inequalities | |

2.8.3. | Further Graphing of Two-Variable Linear Inequalities | |

2.8.4. | Solving Systems of Linear Inequalities | |

2.8.5. | Modeling With Two-Variable Linear Inequalities |

3.

Units
12 topics

3.9. Working With Units

3.9.1. | Unit Conversions Using Base Units of Mass | |

3.9.2. | Two-Step Unit Conversions | |

3.9.3. | Unit Conversions Using Base Units of Length | |

3.9.4. | Unit Conversions Using Units of Time | |

3.9.5. | Unit Conversions Using Base Units of Area | |

3.9.6. | Determining Units in Formulas | |

3.9.7. | Selecting Units for Rates of Change | |

3.9.8. | Converting Between Mixed Units | |

3.9.9. | Degrees of Accuracy |

3.10. Direct and Inverse Variation

3.10.1. | Inverse Variation | |

3.10.2. | Modeling with Direct Variation | |

3.10.3. | Modeling With Inverse Variation |

4.

Radical Expressions
11 topics

4.11. Radical Expressions

4.11.1. | The Square Root of a Perfect Square With Algebraic Expressions | |

4.11.2. | The Square Root of a Perfect Square With Domain Restrictions | |

4.11.3. | The Cube Root of a Perfect Cube With Algebraic Expressions | |

4.11.4. | Simplifying Square Root Expressions Using the Product Rule | |

4.11.5. | Combining Radical Expressions Using the Product Rule | |

4.11.6. | Applying the Quotient Rule for Radicals to Algebraic Expressions | |

4.11.7. | Evaluating Algebraic Radical Expressions | |

4.11.8. | Adding and Subtracting Radical Expressions | |

4.11.9. | Rationalizing Denominators of Algebraic Expressions | |

4.11.10. | Rationalizing Denominators With Two Terms | |

4.11.11. | Solving Radical Equations |

5.

Rational Expressions & Equations
7 topics

5.12. Rational Expressions

5.12.1. | Equivalent Expressions With Fractions | |

5.12.2. | Simplifying Rational Expressions | |

5.12.3. | Simplifying Rational Expressions by Factoring |

5.13. Rational Equations

5.13.1. | Solving Rational Equations Containing One Fractional Term | |

5.13.2. | Solving Rational Equations Using Cross-Multiplication | |

5.13.3. | Solving Rational Equations Containing Binomials Using Cross-Multiplication | |

5.13.4. | Solving Rational Equations Using the Flip Method |

6.

Functions
17 topics

6.14. Functions

6.14.1. | Introduction to Functions | |

6.14.2. | Visual Representations of Functions | |

6.14.3. | Graphs of Functions | |

6.14.4. | The Domain of a Function | |

6.14.5. | The Vertical Line Test | |

6.14.6. | Global Extrema of Functions | |

6.14.7. | End Behavior of Functions | |

6.14.8. | The Range of a Function | |

6.14.9. | The Range of a Function: Advanced Cases | |

6.14.10. | The Roots of a Function | |

6.14.11. | Increasing and Decreasing Functions | |

6.14.12. | Piecewise Functions | |

6.14.13. | Modeling With Linear Functions | |

6.14.14. | The Arithmetic of Functions | |

6.14.15. | Composition of Functions | |

6.14.16. | Finding Algebraic Expressions of Composite Functions | |

6.14.17. | Introduction to Inverse Functions |

7.

Absolute Value
12 topics

7.15. Absolute Value Expressions, Equations & Inequalities

7.15.1. | Evaluating Absolute Value Expressions | |

7.15.2. | Rules of Absolute Value | |

7.15.3. | Further Rules of Absolute Value | |

7.15.4. | Absolute Value Equations | |

7.15.5. | Solving Equations Connecting Absolute Value and Linear Functions | |

7.15.6. | Absolute Value Inequalities |

7.16. Absolute Value Functions

7.16.1. | Absolute Value Graphs | |

7.16.2. | Vertical Reflections of Absolute Value Graphs | |

7.16.3. | Stretches of Absolute Value Graphs | |

7.16.4. | Combining Transformations of Absolute Value Graphs | |

7.16.5. | Domain and Range of Absolute Value Functions | |

7.16.6. | Roots of Absolute Value Functions |

8.

Exponential Functions
22 topics

8.17. Rules of Exponents

8.17.1. | Writing Radical Expressions Using Fractional Exponents | |

8.17.2. | The Product Rule for Exponents With Algebraic Expressions | |

8.17.3. | The Quotient Rule for Exponents With Algebraic Expressions | |

8.17.4. | The Power Rule for Exponents With Algebraic Expressions | |

8.17.5. | The Power of Product Rule With Algebraic Expressions | |

8.17.6. | The Power of Quotient Rule With Algebraic Expressions | |

8.17.7. | Combining the Rules of Exponents With Algebraic Expressions |

8.18. Exponential Expressions & Equations

8.18.1. | Solving Exponential Equations with Integer Solutions | |

8.18.2. | Solving Exponential Equations with Fractional Solutions | |

8.18.3. | Creating Exponential Growth Expressions | |

8.18.4. | Creating Exponential Decay Expressions |

8.19. Exponential Functions

8.19.1. | Exponential Functions | |

8.19.2. | Modeling Exponential Growth With Functions | |

8.19.3. | Interpreting Exponential Growth | |

8.19.4. | Solving Exponential Growth Problems | |

8.19.5. | Modeling Exponential Decay With Functions | |

8.19.6. | Interpreting Exponential Decay | |

8.19.7. | Solving Exponential Decay Problems | |

8.19.8. | Linear vs. Exponential Growth and Decay | |

8.19.9. | Linear vs. Exponential Growth and Decay Models | |

8.19.10. | Graphing Exponential Growth Functions | |

8.19.11. | Graphing Exponential Decay Functions |

9.

Polynomials
19 topics

9.20. Polynomials

9.20.1. | Introduction to Polynomials | |

9.20.2. | The Degree of a Polynomial | |

9.20.3. | Simplifying Polynomials | |

9.20.4. | The Distributive Law for Polynomials | |

9.20.5. | Adding and Subtracting Polynomials | |

9.20.6. | Monomials, Binomials and Trinomials | |

9.20.7. | Multiplying Binomials | |

9.20.8. | Multiplying Polynomials | |

9.20.9. | Squaring Binomials | |

9.20.10. | Expanding Binomials Using Pascal's Triangle | |

9.20.11. | The Difference of Squares Formula |

9.21. Factoring Polynomials

9.21.1. | The Greatest Common Factor of Two Monomials | |

9.21.2. | Factoring Simple Polynomials Using Greatest Common Factors | |

9.21.3. | Factoring Perfect Square Trinomials | |

9.21.4. | Factoring Perfect Square Trinomials With Leading Coefficients | |

9.21.5. | Factoring Differences of Squares | |

9.21.6. | Factoring Trinomials | |

9.21.7. | Factoring Trinomials Using Common Factors | |

9.21.8. | Factoring Trinomials With Leading Coefficients |

10.

Quadratic Equations & Functions
33 topics

10.22. Quadratic Equations

10.22.1. | Introduction to Quadratic Equations | |

10.22.2. | Solving Perfect Square Quadratic Equations | |

10.22.3. | Perfect Square Quadratic Equations with One Solution or No Solutions | |

10.22.4. | The Zero Product Rule for Solving Quadratic Equations | |

10.22.5. | Solving Quadratic Equations Using a Difference of Squares | |

10.22.6. | Solving Quadratic Equations with No Constant Term | |

10.22.7. | Solving Quadratic Equations by Factoring | |

10.22.8. | Solving Quadratic Equations with Leading Coefficients by Factoring | |

10.22.9. | Completing the Square | |

10.22.10. | Completing the Square With Odd Linear Terms | |

10.22.11. | Completing the Square With Leading Coefficients | |

10.22.12. | Solving Quadratic Equations by Completing the Square | |

10.22.13. | Solving Quadratic Equations With Leading Coefficients by Completing the Square | |

10.22.14. | The Quadratic Formula | |

10.22.15. | The Discriminant of a Quadratic Equation | |

10.22.16. | Modeling With Quadratic Equations |

10.23. Quadratic Functions

10.23.1. | Graphing Elementary Quadratic Functions | |

10.23.2. | Vertical Reflections of Quadratic Functions | |

10.23.3. | Graphs of General Quadratic Functions | |

10.23.4. | Roots of Quadratic Functions | |

10.23.5. | The Discriminant of a Quadratic Function | |

10.23.6. | Calculating the Axis of Symmetry of a Parabola | |

10.23.7. | The Average of the Roots Formula | |

10.23.8. | The Vertex Form of a Parabola | |

10.23.9. | Writing the Equation of a Parabola in Vertex Form | |

10.23.10. | Domain and Range of Quadratic Functions | |

10.23.11. | Finding Intersections of Lines and Quadratic Functions |

10.24. Modeling With Quadratic Functions

10.24.1. | Modeling Downwards Vertical Motion | |

10.24.2. | Modeling Upwards Vertical Motion | |

10.24.3. | Vertical Motion | |

10.24.4. | Revenue, Cost, and Profit Functions | |

10.24.5. | Constructing Revenue, Cost, and Profit Functions | |

10.24.6. | Maximizing Profit and Break-Even Points |

11.

Sequences
18 topics

11.25. Introduction to Sequences

11.25.1. | Introduction to Sequences | |

11.25.2. | Recursive Sequences | |

11.25.3. | Fibonacci Sequences |

11.26. Arithmetic Sequences

11.26.1. | Arithmetic Sequences | |

11.26.2. | Recursive Formulas for Arithmetic Sequences | |

11.26.3. | The Nth Term of an Arithmetic Sequence | |

11.26.4. | Translating Between Explicit and Recursive Formulas for Arithmetic Sequences | |

11.26.5. | Finding the Common Difference of an Arithmetic Sequence Given Two Terms | |

11.26.6. | Finding the Nth Term of an Arithmetic Sequence Given Two Terms | |

11.26.7. | Determining Indexes of Terms in Arithmetic Sequences | |

11.26.8. | Solving for Variables in Arithmetic Sequences | |

11.26.9. | Modeling With Arithmetic Sequences |

11.27. Geometric Sequences

11.27.1. | Introduction to Geometric Sequences | |

11.27.2. | The Recursive Formula for a Geometric Sequence | |

11.27.3. | Finding the Nth Term of a Geometric Sequence | |

11.27.4. | Translating Between Explicit and Recursive Formulas for Geometric Sequences | |

11.27.5. | Finding the Common Ratio of a Geometric Sequence Given Two Terms | |

11.27.6. | Finding the Index of a Term in a Geometric Sequence |