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

*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**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*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**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*

*Greatest Common Factor (GCF)*

Difference of Squares

"Easy" Quadratic Factoring

"Hard" Quadratic Factoring

Grouping

Zero-Product Property*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*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

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

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

*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
*Multipliers*

Exponential Growth

Exponential Decay

Simple vs. Compound Interest

Compound Interest by Time Period

Continuously-Compounded Interest

__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*Simplifying Rational Expressions*

Excluded Values for Rational Expressions* *

*Multiplying Rational Expressions*

*Complex Rational Fractions*

Adding and Subtracting Rational Expressions

*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
*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 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= **ta**n 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 (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*

*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: 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*

*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*

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__

Calculating Slope from a Pair of Points

Characteristics of Horizontal and Vertical Lines

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

__SEQUENCES AND SERIES__

Calculating the Sum of an Arithmetic Series

Graphing Arithmetic Sequences

Using Sigma Notation

Finding the Terms of a Geometric Sequence

__LINEAR SYSTEMS__

__FUNCTIONS__

Graphs of Functions

Transformations of Functions

Graphing a Piecewise Function

Function Operations

Inverse Functions

Characteristics of an Inverse Function

__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*

*Exponential
Equations*

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

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

__FACTORING__

Difference of Squares

"Easy" Quadratic Factoring

"Hard" Quadratic Factoring

Grouping

Zero-Product Property

__RADICALS__

*Simplifying Radical ExpressionsFinding Roots of Negative NumbersAdding and Subtracting Radical ExpressionsMultiplying Radical ExpressionsRationalizing 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

Finding x-Intercepts from Vertex Form

Finding the y-Intercept from Vertex Form

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*

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*

*Logarithmic and Exponential 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*

Exponential Growth

Exponential Decay

Simple vs. Compound Interest

Compound Interest by Time Period

Continuously-Compounded Interest

*Roots 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

U-Turns on Polynomial Graphs

Graping Root Multiplicity

Graphing Polynomial Functions

Determining the Polynomial Function from Its Graph

RATIONAL FUNCTIONS

*Rational Expressions*

Excluded Values for Rational Expressions

Adding and Subtracting Rational Expressions

*Rational Functions*

x-Intercepts of Rational Functions

CONIC SECTIONS

Standard Equation of a Circle

Characteristics of an Ellipse

Standard Equation of an Ellipse

Characteristics of a Hyperbola

Standard Equation of a Hyperbola

* 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

* 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

* 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

* Polynomial End Behavior

* U-Turns on Polynomial Graphs

* Graphing Root Multiplicity

* Graphing Polynomial Functions

* Determining the Polynomial Function from a Graph

* 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

* x-Intercepts of Rational Functions

Graphing Rational Functions

* 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

* 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

* 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

* 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*

*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
AnglesFinding
Trigonometric Functions of Any Angle*

*Trigonometric
Identities*

*The
Fundamental Trigonometric Identities*

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*

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

*Inverse Trigonometric Functions*

Domain and Range of Inverse Trigonometric Functions

Composition of Functions with Inverse Trigonometry I: Unit Circle

*Solving Oblique Triangles*

Using the Law of Sines (AAS/ASA)

The Ambiguous Case of the Law of Sines I (SSA)

Using the Law of Cosines (SSS)

Using the Law of Cosines (SAS)

Heron's Area Formula (SSS)

*Solving Trigonometric Equations*

Solving Trigonometric Equations: Square Roots

*Special Trigonometric Formulas*

Problems Using Sum and Difference Formulas

Double-Angle Formulas

* 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