WELCOME TO
MR. LIPP'S "SOLVE" VIDEO TUTORIALS
"Student-Owned Learning through Video Education"

Mr. Michael Lipp is a teacher at Douglas Anderson School of the Arts in Jacksonville, Florida.
These videos were created as a resource for his students in Algebra II Honors and Pre-Calculus,
but Mr. Lipp invites any students needing assistance in those subjects to view them as well.

PLEASE NOTE:
This page is under construction.
Links to videos will be added as they are created.



Click here to go directly to PRE-CALCULUS


ALGEBRA II HONORS

LINEAR EQUATIONS

Slope

Finding Slope from a Graph
Calculating Slope from a Pair of Points
Characteristics of Horizontal and Vertical Lines


Forms of a Linear Equation

Graphing with the Slope-Intercept Form of a Line
Converting Standard Form to Slope-Intercept Form
Finding the X and Y-Intercepts of a Line
Using the Point-Slope Formula
Finding the Equation of a Line from Two Points
Solving Problems with Parallel and Perpendicular Lines


Linear Inequalities

Graping Linear Inequalities

SEQUENCES AND SERIES

Finding the Terms of an Arithmetic Sequence
Calculating the Sum of an Arithmetic Series
Graphing Arithmetic Sequences
Using Sigma Notation
Finding the Terms of a Geometric Sequence

LINEAR SYSTEMS

Solving Linear Systems by Graphing
Solving Linear Systems by Substitution I
Solving Linear Systems by Substitution II
Solving Linear Systems by Elimination I
Solving Linear Systems by Elimination II
Solving Word Problems Using Linear Systems
Graphing Systems of Linear Inequalities
Solving Linear Systems of Three Variables

FUNCTIONS

Introduction to Functions

Functions, Domain, and Range
Finding Domain Restricitions of a Basic Function
Notating and Evaluating a Function
Evaluating a Piecewise Function

Graphs of Functions


Using the Vertical-Line Test
Using Interval Notation
Finding the Domain and Range of a Graphed Function

Transformations of Functions


The Graphs of the Basic Parent Functions
Transformations I: Vertical Translation
Transformations II: Horizontal Translation
Transformations III: Vertical Reflection
 Transformations V: Vertical Stretches and Compressions
Graphing a Transformed Function
Graphing a Piecewise Function


Function Operations


Adding and Subtracting Functions
Multiplying and Dividing Functions
Finding the Composition of Functions

Inverse Functions


Characteristics of an Inverse Function

Finding Inverse Functions
Verifying Inverse Functions Algebraically
Graphing Inverse Functions
Using the Horizontal-Line Test

EXPONENTS

Exponential Expressions

Properties of Exponents: Product of Powers
Multiplying Polynomials
Properties of Exponents: Quotient of Powers
Properties of Exponents: Power of a Power
Properties of Exponents: Power of a Product or Quotient
Simplifying Combined Properties of Exponents Expressions
Zero Power
Negative Exponents

Simplifying Expressions with Negative Exponents
Rational (Fraction) Exponents
Simplifying Expressions with Rational (Fraction) Exponents

Exponential Equations

The One-to-One Property of Exponents I
The One-to-One Property of Exponents II

FACTORING

Greatest Common Factor (GCF)
Difference of Squares
"Easy" Quadratic Factoring
"Hard" Quadratic Factoring
Grouping
Zero-Product Property

RADICALS

Simplifying Radical Expressions
Finding Roots of Negative Numbers
Adding and Subtracting Radical Expressions
Multiplying Radical Expressions
Rationalizing Radical Denominators

IMAGINARY AND COMPLEX NUMBERS

Simplifying Square Roots of Negative Numbers Using i
Powers of i
Complex Numbers and Standard Form
Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
Rationalizing Imaginary Denominators
The Discriminant and Complex Quadratic Roots

QUADRATIC FUNCTIONS

Graphs of Quadratic Functions
 
Properties of Quadratic Function Graphs
Translating Quadratic Funtions
Reflecting Quadratic Functions
Stretching and Compressing Quadratic Functions
 

Vertex Form of a Quadratic Function
 
Vertex Form of a Quadratic Function
Finding x-Intercepts from Vertex Form
 Finding the y-Intercept from Vertex Form
 
Standard Form of a Quadratic Function
 
Standard Form of a Quadratic Function
Vertex and Axis from of a Quadratic Function in Standard Form
Finding Intercepts from Standard Form
The Quadratic Formula
Completing the Square I

LOGARITHMS

Properties of Logarithms

Converting Between Exponential and Logarithmic Expressions
Common and Natural Logarithms
Evaluating Simple Logarithms
Special Logarithmic Identities
Power Property of Logarithms
Quotient Property of Logarithms
Exponent Property of Logarithms
Expanding and Condensing Logarithmic Expressions
Change-of-Base Formula

Logarithmic Equations

The One-to-One Property of Logarithms I
The One-to-One Property of Logarithms II

Logarithmic and Exponential Functions

The Graph of Logarithmic Functions
The Graph of Exponential Functions
Logarithmic and Exponential Functions as Inverses
Finding the Inverse of a Logarithmic Function
Finding the Inverse of an Exponential Function

Exponential Growth and Decay

Multipliers
Exponential Growth
Exponential Decay
Simple vs. Compound Interest
Compound Interest by Time Period
Continuously-Compounded Interest

POLYNOMIALS

Roots of Polynomials

Characteristics of Polynomials
Finding Real Roots of Polynomials
Finding the y-Intercept of a Polynomial
Polynomial Root Multiplicity
Long Division of Polynomials
Synthetic Division of Polynomials
The Remainder Theorem

Graphs of Polynomial Functions

Polynomial End Behavior
U-Turns on Polynomial Graphs
Graping Root Multiplicity
Graphing Polynomial Functions
Determining the Polynomial Function from Its Graph

RATIONAL FUNCTIONS

Rational Expressions

Simplifying Rational Expressions
Excluded Values for Rational Expressions

Multiplying Rational Expressions
Complex Rational Fractions
Adding and Subtracting Rational Expressions

Rational Functions

Removable Discontinuities or "Holes" in Rational Functions
x-Intercepts of Rational Functions
y-Intercepts of Rational Functions
Vertical Asymptotes of Rational Functions
Horizontal Asymptotes of Rational Functions

CONIC SECTIONS

Classifying Conics from the General Formula
Standard Equation of a Circle
Characteristics of an Ellipse
Standard Equation of an Ellipse
Characteristics of a Hyperbola
Standard Equation of a Hyperbola



PRE-CALCULUS
* Algebra II Honors Videos

FUNCTIONS

Introduction to Functions

* Functions, Domain, and Range
* Notating and Evaluating a Function
* Finding Domain Restricitions of a Basic Function
* Evaluating a Piecewise Function
Evaluating a Difference Quotient
Finding the Zeroes of a Function
Even and Odd Functions

Graphs of Functions

* Using the Vertical-Line Test
* Using Interval Notation
* Finding the Domain and Range of a Graphed Function
Increasing Functions, Decreasing Functions, Maxima, and Minima
* Graphing a Piecewise Function

Transformations of Functions

* The Graphs of the Basic Parent Functions
* Transformations I: Vertical Translation
* Transformations II: Horizontal Translation
* Transformations III: Vertical Reflection
Transformations IV: Horizontal Reflection
* Transformations V: Vertical Stretches and Compressions
Transformations VI: Horizontal Stretches and Compressions
* Graphing a Transformed Function

Function Operations

* Adding and Subtracting Functions
* Multiplying and Dividing Functions
* Finding the Composition of Functions
Domain Restrictions of a Composite Function

Inverse Functions

* Characteristics of an Inverse Function
* Finding Inverse Functions
* Verifying Inverse Functions Algebraically
* Graphing Inverse Functions
 * Using the Horizontal-Line Test

QUADRATIC FUNCTIONS
 
Vertex Form of a Quadratic Function
 
* Vertex Form of a Quadratic Function
* Finding x-Intercepts from Vertex Form
* Finding the y-Intercept from Vertex Form
 
Standard Form of a Quadratic Function
 
* Standard Form of a Quadratic Function
* Vertex and Axis from of a Quadratic Function in Standard Form
* Finding Intercepts from Standard Form
* The Quadratic Formula
* Completing the Square I
Completing the Square II
 
POLYNOMIAL FUNCTIONS
 
Roots of Polynomials
 
* Characteristics of Polynomials
* Finding Real Roots of Polynomials
* Finding the y-Intercept of a Polynomial
* Polynomial Root Multiplicity
* Long Division of Polynomials
* Synthetic Division of Polynomials
* The Remainder Theorem
The Rational Zero Test
Complex Zeroes of Polynomials
Descartes's Rule of Signs
Upper and Lower Bounds of Polynomial Roots
Finding the Zeroes of a Polynomial Function
 
Graphs of Polynomial Functions
 
* Polynomial End Behavior
* U-Turns on Polynomial Graphs
* Graphing Root Multiplicity
* Graphing Polynomial Functions
* Determining the Polynomial Function from a Graph

IMAGINARY AND COMPLEX NUMBERS
 
* Simplifying Square Roots of Negative Numbers Using i
* Powers of i
* Complex Numbers and Standard Form
* Adding and Subtracting Complex Numbers
* Multiplying Complex Numbers
* Rationalizing Imaginary Denominators
* The Discriminant and Complex Quadratic Roots
 
RATIONAL FUNCTIONS
 
* Removable Discontinuities or "Holes" in Rational Functions
* x-Intercepts of Rational Functions
* y-Intercepts of Rational Functions
* Vertical Asymptotes of Rational Functions
* Horizontal Asymptotes of Rational Functions
Oblique or Slant Asymptotes of Rational Functions
 Graphing Rational Functions


LOGARITHMIC AND EXPONENTIAL FUNCTIONS
 
Properties of Logarithms
 
* Converting Between Exponential and Logarithmic Expressions
* Common and Natural Logarithms
* Evaluating Simple Logarithms
* Special Logarithmic Identities
* Power Property of Logarithms
* Quotient Property of Logarithms
* Exponent Property of Logarithms
* Expanding and Condensing Logarithmic Expressions
* Change-of-Base Formula
 
Logarithmic and Exponential Equations
 
* The One-to-One Property of Logarithms I
* The One-to-One Property of Logarithms II
* The One-to-One Property of Exponents I
* The One-to-One Property of Exponents II
Solving Logarithmic and Exponential Equations


Logarithmic and Exponential Functions
 
* The Graph of Logarithmic Functions
* The Graph of Exponential Functions
Characteristics of a Transformed Logarithmic Function
Characteristics of a Transformed Exponential Function
* Logarithmic and Exponential Functions as Inverses
* Finding the Inverse of a Logarithmic Function
* Finding the Inverse of an Exponential Function
 
Exponential Growth and Decay
 
* Multipliers
* Exponential Growth
* Exponential Decay
* Simple vs. Compound Interest
* Compound Interest by Time Period
* Continuously-Compounded Interest
Exponential Growth and Decay Using the Natural Base, e


TRIGONOMETRY

Right Triangle Trigonometry

Right Triangle Trigonometry
Solving Right Triangles
Cofunctions of Complementary Angles
Special Right Triangles

Angle Measurement on the Coordinate Plane

Angles on the Coordinate Plane
Measuring Angles in Radians
Angles on the Unit Circle in Radians
Coterminal Angles in Radians
Complementary and Supplementary Angles in Radians
Working with DMS (Degrees, Minutes, Seconds) Form

The Unit Circle

Standard Coordinates in Quadrant I of the Unit Circle
Standard Coordinates in Quadrants II, III, and IV of the Unit Circle
sin, cos, and tan for Standard Unit Circle Angles
cot, sec, and csc for Standard Unit Circle Angles
Sign of Trigonometric Functions by Quadrant
Domain, Range, and Period of sin and cos
Even and Odd Trigonometric Functions

Trigonometric Functions of Any Angle

Reference Angles
Finding Trigonometric Functions of Any Angle

Trigonometric Identities

The Fundamental Trigonometric Identities
Using Identities to Find Trigonometric Functions of Any Angle
Cofunction and Even-Odd Identities

Verifying Trigonometric Identities
Simplifying Trigonometric Expressions
Factoring Trigonometric Expressions
Combining Trigonometric Fractions
Using Trigonometric Conjugates
Common Techniques for Verifying Trigonometric Identities
Combining Trigonometric Fractions in Verification
Using Trigonometric Conjugates in Verification
Converting to sin and cos in Verification

Graphs of Trigonometric Functions

Graphs of  y= sin x and y= cos x
Amplitude and Period of sin x and cos x
Stretching and Compressing sin x and cos x
Sketching Transformed Graphs of sin x and cos x Using Key Points
Graphs of  y= tan x and y= cot x
Sketching Transformed Graphs of tan x and cot x Using Key Points
Graphs of  y= sec x and y= csc x
Sketching Transformed Graphs of sec x and csc x Using Key Points

Inverse Trigonometric Functions

Inverse Trigonometric Functions (arcsin, arccos, arctan)
Domain and Range of Inverse Trigonometric Functions
Composition of Functions with Inverse Trigonometry I: Unit Circle
Composition of Functions with Inverse Trigonometry II: Non-Unit Circle
Composition of Functions with Inverse Trigonometry III: Algebraic

Solving Oblique Triangles

Law of Sines vs. Law of Cosines
Using the Law of Sines (AAS/ASA)
The Ambiguous Case of the Law of Sines I (SSA)
The Ambiguous Case of the Law of Sines II (SSA)
Finding the Area of a Triangle (SAS)
Using the Law of Cosines (SSS)
Using the Law of Cosines (SAS)
Heron's Area Formula (SSS)

Solving Trigonometric Equations

Solving Trigonometric Equations: Like Terms
Solving Trigonometric Equations: Square Roots
Solving Trigonometric Equations: Factoring and Quadratics
Solving Trigonometric Equations: Rewriting as a Single Function
Solving Trigonometric Equations: Squaring
Solving Trigonometric Equations: Multiple Angles
Solving Trigonometric Equations: Using Inverses

Special Trigonometric Formulas

Sum and Difference Formulas
Problems Using Sum and Difference Formulas
Double-Angle Formulas
Problems Using Double-Angle Formulas
Power-Reducing Formulas
Problems Using Power-Reducing Formulas
Half-Angle Formulas
Problems Using Half-Angle Formulas

CONIC SECTIONS

* Classifying Conics from the General Formula
* Standard Equation of a Circle
Characteristics of a Parabola
Standard Equation of a Parabola
Converting the General Equation of a Parabola
* Characteristics of an Ellipse
* Standard Equation of an Ellipse
Foci of an Ellipse
Converting the General Equation of an Ellipse
Eccentricity of an Ellipse
* Characteristics of a Hyperbola
* Standard Equation of a Hyperbola
Foci of a Hyperbola
Converting the General Equation of a Hyperbola
Eccentricity of a Hyperbola
Asymptotes of a Hyperbola