Learn Algebra 2 – Free Course with Videos and Guided Notes
Build a strong foundation in Algebra 2 with structured video lessons, guided notes, and worked examples. Covering linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions, as well as complex numbers, rational exponents, radicals, and sequences and series, this free course builds understanding and confidence through clear, step-by-step instruction.
Chapter 1 - Linear Functions
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Engage actively by completing the notes during the lesson.
Review your completed notes as a study resource for exams.
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In this video, you'll learn the most important parent functions used throughout algebra and precalculus. We'll explore thirteen common parent functions, examine their graphs and key characteristics, and see how they form the foundation for understanding more complex functions.
In this video, you'll learn how transformations change the graph of a function. We'll investigate vertical and horizontal shifts, stretches, compressions, and reflections and develop rules for predicting how each transformation affects a graph and its equation.
In this video, you'll learn a systematic process for graphing transformed functions. We'll start with parent functions and apply scaling, translations, and reflections step by step to graph more complicated functions.
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In this video, you'll learn two common methods for solving systems of equations in two variables: substitution and elimination. We'll follow a step-by-step process for each method, solve systems of linear equations, and verify solutions by checking them in the original equations.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 2 - Quadratic Functions
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Review your completed notes as a study resource for exams.
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In this video, you'll learn the essential geometry and equations of parabolas. We'll define a parabola using its focus and directrix, identify vertices, foci, axes of symmetry, and directrices, develop the standard forms of parabola equations, and work through examples involving graphing parabolas and finding equations from given geometric information.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 3 - Quadratic Equations and Complex Numbers
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In this video, you'll learn how to factor quadratic functions. We'll factor quadratics of the form x² + bx + c and ax² + bx + c, develop strategies for finding factors, and see how factoring can be used to find zeros and graph quadratic functions.
In this video, you'll learn how to solve quadratic equations using the square root property. We'll solve equations of the form ax² = c and (ax + b)² = c, isolate squared expressions, and use square roots to find all solutions.
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In this video, you'll learn how to solve quadratic equations by completing the square. We'll transform quadratic equations into perfect square trinomials and use the square root property to find exact solutions.
In this video, you'll learn how to convert a quadratic equation from standard form to vertex form. We'll use both the vertex formula and completing the square to rewrite quadratic equations and identify key graphing features such as the vertex.
In this video, you'll learn how to recognize and factor special quadratic expressions. We'll factor differences of two squares, factor perfect square trinomials, and identify patterns that make factoring faster and more efficient.
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In this video, you'll learn how to solve quadratic equations using the quadratic formula. We'll apply the formula to find rational, irrational, and complex solutions and discuss when the quadratic formula is the most effective solution method.
In this video, you'll learn how the discriminant can be used to determine the number and type of solutions of a quadratic equation. We'll calculate the discriminant and interpret whether a quadratic equation has two real solutions, one repeated solution, or two complex solutions.
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Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 4 - Polynomial Functions
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Review your completed notes as a study resource for exams.
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In this video, you'll learn how to multiply polynomials. We'll use the distributive property to multiply monomials and polynomials, multiply two polynomials together, and combine like terms to simplify the result.
In this video, you'll learn how to divide polynomials using long division. We'll divide polynomials by linear expressions, identify the quotient and remainder, and write answers in simplified form.
In this video, you'll learn how to divide polynomials using synthetic division. We'll use synthetic division to find quotients and remainders, work with missing terms, and interpret the results.
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In this video, you'll learn how to factor polynomials using the greatest common factor (GCF). We'll identify common numerical and variable factors, factor expressions completely, and simplify the results when possible.
In this video, you'll learn how to factor polynomials by grouping. We'll factor four-term polynomials by grouping terms, finding common factors, and factoring out common binomials.
In this video, you'll learn how to factor sums and differences of cubes. We'll identify perfect cubes, apply the appropriate factoring formulas, and simplify the resulting expressions.
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In this video, you'll learn how to use the Remainder Theorem and Factor Theorem. We'll evaluate polynomials efficiently, determine remainders without performing division, and identify factors and zeros of polynomial functions.
In this video, you'll learn how to use the Rational Zeros Theorem to find the zeros of polynomial functions. We'll identify possible rational zeros, test candidates using synthetic division, and factor polynomials completely.
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In this video, you'll learn how to graph polynomial functions. We'll determine end behavior, find zeros and their multiplicities, and use this information to sketch accurate graphs of polynomials.
In this video, you'll learn how to determine whether a function is even, odd, or neither. We'll explore the algebraic and graphical properties of even and odd functions, examine symmetry, and apply a systematic process for classifying functions.
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Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 5 - Rational Exponents and Radical Functions
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Review your completed notes as a study resource for exams.
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In this video, you'll learn the seven fundamental laws of exponents. We'll simplify expressions using the product, quotient, power, zero exponent, negative exponent, power of a product, and power of a quotient rules, then apply multiple exponent rules together in more complex examples.
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In this video, you'll learn what inverse functions are and how they undo the action of another function. We'll develop the notation for inverse functions, explore their key properties, and find inverses from tables and graphs.
In this video, you'll learn a step-by-step process for finding the inverse of a function algebraically. We'll interchange variables, solve for the inverse function, and work through examples involving linear, radical, polynomial, and rational functions.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 6 - Exponential and Logarithmic Functions
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Review your completed notes as a study resource for exams.
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In this video, you'll learn what exponential functions are and how they differ from linear functions. We'll explore the general form of an exponential function, compare exponential and linear growth, distinguish between exponential growth and decay, and discuss real-world applications of exponential models.
In this video, you'll learn how exponential functions are used to model real-world situations. We'll solve growth and decay problems involving population growth, medication decay, half-life, bacterial growth, and continuous exponential models.
In this video, you'll learn how compound interest works. We'll use formulas for periodic and continuous compounding, calculate future values of investments, determine present values, and solve for the time required for investments to reach a target amount.
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In this video, you'll learn about the natural exponential function and the natural logarithm. We'll explore the number e, examine the relationship between y = e^x and y = ln(x), discuss their properties, and see why these functions are important in mathematics, science, and engineering.
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In this video, you'll learn how to evaluate logarithms. We'll rewrite logarithmic expressions in exponential form, interpret logarithms as exponents, and evaluate logarithms with a variety of bases through step-by-step examples.
In this video, you'll learn how to graph logarithmic functions. We'll identify logarithmic growth and decay, determine vertical asymptotes, analyze horizontal and vertical shifts, create tables of values, and sketch logarithmic graphs.
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In this video, you'll learn the key properties of logarithms. We'll use the product, quotient, and power rules to expand and condense logarithmic expressions, apply important logarithmic identities, and work through examples that combine multiple properties.
In this video, you'll learn how to use the change of base formula. We'll rewrite logarithms with different bases using common logarithms or natural logarithms and use a calculator to evaluate logarithmic expressions that cannot be computed directly.
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In this video, you'll learn how to solve exponential equations. We'll solve equations by rewriting both sides with the same base when possible and use logarithms to solve equations when matching bases is not practical.
In this video, you'll learn how to solve logarithmic equations. We'll combine logarithms using logarithmic properties, apply the one-to-one property of logarithms, rewrite logarithmic equations in exponential form, and check for extraneous solutions.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 7 - Rational Functions
Watch the video lessons for each section.
Download the guided notes PDF to follow along as you watch.
Engage actively by completing the notes during the lesson.
Review your completed notes as a study resource for exams.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 8 - Sequences and Series
Watch the video lessons for each section.
Download the guided notes PDF to follow along as you watch.
Engage actively by completing the notes during the lesson.
Review your completed notes as a study resource for exams.
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In this video, you'll learn the fundamentals of sequences, including how to identify terms, find the first several terms of a sequence, develop formulas for the nth term, and calculate partial sums. We'll work with explicit and recursive formulas, recognize common sequence patterns such as arithmetic, geometric, and Fibonacci sequences, and solve examples involving sequence notation and partial sums.
In this video, you'll learn how to use summation (sigma) notation to represent and evaluate series. We'll define the components of sigma notation, evaluate finite sums, write series using summation notation, identify patterns in sequences, and work through examples involving powers, fractions, alternating series, and polynomial expressions.
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In this video, you'll learn how arithmetic sequences are formed and how to work with them using formulas and examples. We'll develop the arithmetic sequence formula, find terms and nth-term formulas, determine whether a sequence is arithmetic, identify common differences, and calculate partial sums of finite arithmetic sequences using the arithmetic series formula.
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In this video, you'll learn how geometric sequences and geometric series work. We'll develop the geometric sequence formula, find terms and nth-term formulas, identify common ratios, determine whether a sequence is geometric, calculate partial sums of finite geometric sequences, and find the sums of infinite geometric series when they converge.
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In this video, you'll learn the fundamentals of sequences, including how to identify terms, find the first several terms of a sequence, develop formulas for the nth term, and calculate partial sums. We'll work with explicit and recursive formulas, recognize common sequence patterns such as arithmetic, geometric, and Fibonacci sequences, and solve examples involving sequence notation and partial sums.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Chapter 9 - Trigonometric Ratios and Functions
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Download the guided notes PDF to follow along as you watch.
Engage actively by completing the notes during the lesson.
Review your completed notes as a study resource for exams.
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In this video, you'll learn the Pythagorean Theorem, one of the most important relationships in geometry and trigonometry. We'll explore how the theorem relates the sides of a right triangle and use it to find missing side lengths through a variety of examples.
In this video, you'll learn how the six trigonometric functions relate the angles of a right triangle to ratios of its sides. We'll define sine, cosine, tangent, cosecant, secant, and cotangent, develop their reciprocal relationships, and use right triangles to evaluate each trigonometric function.
In this video, you'll learn the special side relationships found in 45-45-90 and 30-60-90 triangles. We'll develop formulas for finding unknown side lengths, explore the exact values of related trigonometric functions, and see how these special triangles simplify many trigonometry problems.
In this video, you'll learn how to solve a right triangle by finding all unknown side lengths and angle measures. We'll examine common problem types, use the Pythagorean Theorem and trigonometric ratios to determine missing values, and work through several complete examples.
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In this video, you'll learn how to convert between degrees and radians. We'll develop the conversion formulas, understand where they come from, and work through examples that illustrate how to move between these two angle measurement systems.
In this video, you'll learn how angles are represented in standard position on the coordinate plane and how to determine coterminal angles. We'll identify positive and negative angles, develop methods for finding coterminal angles, and work through several examples.
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In this video, you'll learn what a reference angle is and why it plays an important role in trigonometry. We'll examine how reference angles are defined in each quadrant, develop formulas for finding them, and work through several examples involving angles measured in both degrees and radians.
In this video, you'll learn how trigonometric functions can be extended from right triangles to real numbers using the unit circle. We'll develop the definitions of the six trigonometric functions in terms of unit circle coordinates and evaluate trigonometric functions for points on the unit circle.
In this video, you'll learn the fundamental ideas behind the unit circle and how it connects geometry and trigonometry. We'll review the equation of a circle, develop the equation of the unit circle, identify quadrant points, and use the unit circle equation to find coordinates of points on the circle.
In this video, you'll learn the special angles and coordinate points that appear most frequently in trigonometry. We'll review the quadrants of the unit circle, develop the coordinates associated with 30°, 45°, and 60°, and identify the key angles and points that are essential to memorize.
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In this video, you'll learn how the sine and cosine graphs are connected to the unit circle and how they form the foundation of sinusoidal functions. We'll develop the graphs of sine and cosine, introduce amplitude, period, phase shift, and midline, and use these ideas to graph sinusoidal functions.
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In this video, you'll learn how to graph the tangent function and identify its key features. We'll develop the graph using the unit circle, determine where tangent is undefined, locate vertical asymptotes, examine its period, and graph general tangent functions involving horizontal and vertical transformations.
In this video, you'll learn how to graph the reciprocal trigonometric functions. We'll express cosecant, secant, and cotangent in terms of sine, cosine, and tangent, determine where each function is undefined, identify vertical asymptotes and periods, and use these properties to sketch their graphs.
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In this video, you'll learn how sinusoidal functions can be used to model real-world periodic behavior. We'll analyze the motion of a Ferris wheel rider, determine the amplitude, period, phase shift, and midline of the model, and develop both sine and cosine equations that describe the rider's height over time.
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In this video, you'll learn the most important trigonometric identities used throughout trigonometry, calculus, physics, and engineering. We'll introduce reciprocal identities, ratio identities, Pythagorean identities, periodicity identities, even-odd identities, cofunction identities, sum and difference formulas, product-to-sum formulas, sum-to-product formulas, and double-angle formulas.
In this video, you'll learn a systematic process for verifying trigonometric identities. We'll discuss how to choose the best side to work on, identify useful algebraic and trigonometric techniques, and apply a step-by-step strategy to verify a variety of increasingly challenging identities.
In this video, you'll learn strategies for rewriting complicated trigonometric expressions in simpler forms. We'll combine trigonometric identities with algebraic techniques such as factoring, common denominators, conjugates, and substitutions to simplify a variety of trigonometric expressions.
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In this video, you'll learn how to evaluate trigonometric functions involving sums and differences of angles. We'll develop the sum and difference formulas for sine, cosine, and tangent and use them to find exact values of trigonometric expressions that cannot be evaluated directly from the unit circle.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
About Dr. Cheryl Hile
Understand The Math was created by Dr. Cheryl Hile, who earned a Ph.D. in Engineering Science and Applied Mathematics from Northwestern University. She has more than 25 years of experience teaching mathematics at the university level, including 20 years at Penn State. The lessons and guided notes on this site are based on materials she developed for her university courses.