Module 2: Radical Equations and Radical Functions

Textbook Section 2.1:  Graphs of the Square Root Functions

Learning Objectives

• Graph and compare square root functions.
• Shift graphs of square root functions.
• Graph square root functions using a graphing calculator.
• Solve real-world problems using square root functions.

Video Lessons

1. Introduction to Square Root and Perfect Squares
2. Graphing the Basic Square Root Function
3. Reflections of the Square Root Function
4. Horizontal and Vertical Shifts of the Square Root Function
5. Horizontal and Vertical Stretches and Compressions of the Square Root Function
6. Function Transformation Summary - The Square Root Function

Video Examples

1. Ex 1:  Graphing a Transformation of the Square Root Function
2. Ex 2:  Graphing a Transformation of the Square Root Function

Section 2.2 Textbook:  Radical Expressions I

Learning objectives

• Use the product and quotient properties of radicals to simplify radicals.
• Add and subtract radical expressions.
• Solve real-world problems using square root functions.

Video Lessons

1. Introduction to Radicals
2. Simplifying Radicals
3. Adding and Subtracting Radicals

Video Examples

1. Ex:  Simplify Square Roots - Perfect Roots
2. Ex:  Simplify Perfect Nth Roots - Radicals
3. Ex:  Simplify Square Roots - Not Perfect Roots
4. Ex:  Simplify a Radical Expression containing Square Roots in the Numerator and Denominator
5. Ex:  Simplify Radicals with the Same Radicand and Different Indexes
6. Ex:  Simplify a Radical Containing a Fraction - Perfect Root
7. Ex:  Simplify Radicals with Variables - Perfect Roots
8. Ex:  Simplify Radicals Containing Variables With Large Exponents - Not Perfect Roots
9. Ex:  Simplify Radicals with Negative Radicands and Odd Indexes
10. Ex:  Simplify Radicals with Variables - Not Perfect Roots
11. Evaluating Radical Expressions on the TI83/84
12. Ex:  Add and Subtract Square Roots - No Simplifying
13. Ex:  Add and Subtract Square Roots
14. Ex:  Add and Subtract Square Roots Containing Variables

Section 2.3 Textbook:  Radical Expressions II

Learning objectives

• Multiply radical expressions.
• Rationalize the denominator.

Video Lessons

1. Introduction to Multiplying Radicals [+]
2. Multiplying Radicals Containing Variables [+]
3. Multiplying Binomials with Radicals [+]
4. Multiplying Conjugates of Radical Expressions [+]
5. Dividing Radicals [+]

Video Examples

1. Ex:  Multiply Square Roots
2. Ex 1:  Multiply Radicals
3. Ex 2:  Multiply Radicals
4. Ex:  Multiply Radicals with Variables
5. Ex:  Radicals Raised to Powers
6. Ex:  Distribution with Square Roots
7. Ex: Multiply Binomials with Square Roots
8. Ex:  Square Binomials With Square Roots
9. Ex:  Multiply Radical Conjugates - Square Roots
10. Ex 1:  Rationalize the Denominator of a Radical Expression
11. Ex 2:  Rationalize the Denominator of a Radical Expression
12. Ex:  Rationalize the Denominator of a Radical Expression - Conjugate

Section 2.5-2.6 Textbook:  The Pythagorean Theorem / Distance Formula / Midpoint
Section 2.5
Section 2.6 

Learning Objectives

• Use the Pythagorean Theorem.
• Use the converse of the Pythagorean Theorem.
• Solve real-world problems using the Pythagorean Theorem and its converse.
• Find the distance between two points in the coordinate plane.
• Find the missing coordinate of a point given the distance from another known point.
• Find the midpoint of a line segment.
• Solve real-world problems using distance and midpoint formulas.

Section 2.7-2.8 Textbook:  Complex Numbers
Section 2.7
Section 2.8 

Learning Objectives

• Write square roots with negative radicands in terms of i
• Recognize and write complex numbers in standard form
• Describe the relationship between the sets of integers, rational numbers, real numbers and complex
• numbers
• Add and subtract complex numbers
• Find the complex conjugate of a complex number
• Multiply and divide complex numbers
• Use your calculator to add, subtract, multiply, and divide complex numbers