College Algebra Tutorials

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Conic Sections: Parabolas, Ellipses, Hyperbolas

Not Created by Me: Great Visual of all the Conic Sections

Parts of a Parabola (Vertex, Focus, Directrix)
The Equation of a Parabola with Vertex at the Origin
Examples of Graphing Parabolas
Determining the Equation of a Parabola

Parts of an Ellipse (Center, Major Axis, Minor Axis, Vertices, Minor Vertices, Foci)
The Equation of an Ellipse with Center at the Origin
Example of Graphing an Ellipse
Re-writing the Equation of an Ellipse Centered at the Origin in a Nice Form

Parts of a Hyperbola (Center, Vertices, Foci, Asymptotes)
The Equation of a Hyperbola with Center at the Origin
The Equations for the Asymptotes of a Hyperbola
Example of Graphing a Hyperbola

Completing the Square to Write the Equation of a Parabola in Standard Form
Completing the Square to Write the Equation of an Ellipse in Standard Form
Completing the Square to Write the Equation of a Hyperbola in Standard Form

Rational Expression (Fraction) Review

Reducing Rational Expressions (Fractions Review) (YouTube)
Multiplying and Dividing Rational Expressions (Fraction Review) (YouTube)
Equivalent Fractions (Fractions Review) (YouTube)
Adding and Subtracting Rational Expressions (Fractions Review) (YouTube)

Old Videos (Need to be redone in YouTube)

Function Basics

Definition of a Function; Introduction to Function Notation (YouTube)
Graphing a Constant Function on a Restricted Domain (YouTube)
Graphing a Linear Function on a Restricted Domain (YouTube)
Graphing a Quadratic Function on a Restricted Domain (YouTube)
Vertical Transformations (on y-values) (YouTube)
Horizontal Transformations (on x-values) (YouTube)
Graphing Functions Using Transformations (YouTube)
Writing the Equation of a Function Given a List of Transformations (YouTube)

Adding, Subtracting, Multiplying, and Dividing Functions (YouTube)
Understanding Composition of Functions with Numeric Examples (YouTube)
Determining the Domain of a Composition of Functions (YouTube)

Definition of an Injective (One-to-One) Function (YouTube)
Definition of an Inverse Function with Basic Examples (YouTube)
Finding the Equation of an Inverse Function (YouTube)
Using Function Composition to Verify that Two Functions are Inverses (YouTube)
Graphing an Inverse Function Using the Original Function Graph (YouTube)

Exponential and Logarithmic Functions

Exponent Review: Zero, Negative, and Fractional Exponents (YouTube)
What is a Logarithm? (YouTube)
The Number e, Common Logarithms, & Natural Logarithms (YouTube)

Basic Exponential Functions (YouTube)
Graphing an Exponential Function Using Transformations (YouTube)

Logarithmic and Exponential Functions are Inverses
Exponential and Logarithmic Functions "Undo" Each Other

Restrictions on Logarithms (YouTube)
Finding the Domain of Functions with Logarithms (YouTube)
Advanced Example: Finding the Domain of Functions with Logarithms (YouTube)

Basic Logarithmic Function Graph (YouTube)

Taking a Logarithm of an Exponential Expression (YouTube)
Solving Basic Exponential Equations (YouTube)

Solving Logarithmic Equations (YouTube)

Function Model for Exponential Growth (YouTube)
Example of Exponential Population Growth (YouTube)

Understanding a Formula for Radioactive Decay and Half-Life (YouTube)
Example of Modeling Radioactive Decay (YouTube)
Example of Modeling Radioactive Decay when Given Mass Percentages (YouTube)

Understanding Newton's Law of Cooling (YouTube)

Factoring Polynomials

Synthetic Division of Polynomials (YouTube)
Using Synthetic Division to Evaluate a Polynomial (YouTube)
How Zeros and Factors of a Polynomial are Related

General Method of Completing the Square (YouTube)
Solving a Quadratic Equation by Using a Square Root (Completing the Square) (YouTube)
Factoring Quadratic Polynomials (YouTube)

Rational Zeros of a Polynomial (YouTube)
Factoring a Polynomial by First Finding a Rational Zero (YouTube)

Polynomial & Rational Functions

Determining What Values Make a Polynomial Zero, Positive, or Negative (YouTube)
Using the Leading Term of a Polynomial to Graph its "Ends" (YouTube)

When a Rational Function is Zero, Not Defined, Positive, or Negative
Finding the x-Intercepts and Vertical Asymptotes of a Rational Function
The "Ends" of a Rational Function - The Horizontal Asymptote
Graphing a Factored Rational Function
Graphing a Non-Factored Rational Function
Graphing a Rational Function Where the Ends are not Horizontal (YouTube)

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