Algebra 2 Video Series

Identify the real number system types—rational, irrational, integers, natural numbers, and whole numbers—and apply their properties, including commutative, associative, distributive, and closure to solve equations and inequalities.

Master solving equations by applying the distributive property, combining like terms, and isolating variables to solve two-step equations, fractions, and proportions, including no and infinite solutions.

Isolate the absolute value, solve for the inside in both positive and negative cases, and check for extraneous solutions in the original equation.

Graph and solve one-variable inequalities on a number line using open or closed dots, parentheses or brackets, and express solutions in interval or set notation, including unions and overlaps.

Learn to solve absolute value inequalities by isolating the absolute value, using the or case and the less-than-or-equal-to case, solving two inequalities, and graphing the intersection with interval notation.

Explore linear functions in standard form and slope-intercept form. Learn to find x-intercepts, y-intercepts, analyze slope as a rate of change, and identify parallel or perpendicular lines.

Learn to find equations of lines using point slope, slope intercept, and standard forms, and apply them to real problems like gym memberships, boat costs, coins, and bike-path modeling.

Learn to solve systems of equations by graphing and substitution, identifying the intersection as the solution and recognizing cases of no solution or infinite solutions, including parallel lines.

Master solving systems by elimination with stacked equations and add/subtract steps, and apply to real-world problems such as break-even, coin counts, car rental costs, and mixture scenarios.

Apply elimination to reduce a three-variable system to two equations, then solve for x, y, z step by step and back-substitute, including recognizing no-solution cases when planes are parallel.

Explore graphing and solving linear inequalities by shading regions, testing points, and using slope-intercept form to determine solutions, including real-world applications like cookie sales.

Graph and shade systems of linear inequalities, find the overlapping solution, and use slope-intercept form with dotted or solid lines to determine feasibility.

Learn how transformations of functions move parent graphs, using the absolute value as a guide. Identify vertex shifts, vertical and horizontal stretches or compressions, and reflections using graphing tools.

Explore how absolute value functions represent distance from zero, graph as a V with a vertex, and use transformations to sketch f(x)=a|x−c|+d, determine domain and range, and shade inequalities.

Explore quadratic functions in standard form and vertex form, learn the axis of symmetry x = -b/(2a), and locate the vertex and intercepts while graphing parabolas.

Learn vertex-form quadratics, identify the vertex and axis of symmetry, and analyze width via vertical stretch or compression, plus reflections and shifts.

Learn how to convert quadratic functions from standard form to vertex form by completing the square, revealing the vertex and enabling easy graphing.

Learn factoring methods across scenarios: extract common factors, apply gcf, use factoring by grouping, and employ product-sum or trial-and-error for three-term quadratics, plus difference of squares for two-term cases.

Master solving quadratic equations by factoring: set to zero, factor the expression, and solve each factor for x using GCF, difference of squares, and multiplicity.

Compare standard, vertex, and factored forms of quadratic functions, and learn to convert between forms with completing the square and factoring to identify vertices, intercepts, and graphs.

Learn to simplify square roots by pulling out the largest perfect square, factoring inside radicals, and combining outside coefficients, with examples and practice from problems 1–6.

Apply the square root method to quadratics with no linear term by isolating x^2, taking square roots, and using plus or minus to find the two solutions.

Learn to form and simplify complex numbers in standard form a plus or minus b i, perform addition, subtraction, multiplication, and division, and rationalize denominators using conjugates.

Derive the quadratic formula by completing the square from a general ax^2+bx+c=0, showing it solves all quadratics, including complex roots, with x = (-b ± the square root of b^2-4ac)/(2a).

Solve quadratic equations efficiently by applying the quadratic formula, setting the equation to zero, identifying a, b, and c, and simplifying radicals to obtain real or complex solutions.

Explore how to solve quadratics using all methods learned, focusing on the discriminant to determine real or complex roots, and applying factoring, graphing, completing the square, and the quadratic formula.

Explore applications of quadratic functions, including geometric problems with rectangles, area calculations, and projectile motion, and learn to solve quadratics via factoring, completing the square, or the quadratic formula.

Master monomials and polynomials by applying product, power, and quotient rules, including negative exponents. Classify by degree and term count as linear, quadratic, cubic, constant, binomial, and trinomial.

Review factoring polynomials in algebra 2 by pulling out the GCF, applying difference and sum of squares and cubes, and factoring trinomials by product-sum or guess-and-check.

Learn to divide polynomials using long division and synthetic division, including pulling out a GCF, factoring, and handling binomial divisors.

Learn how to perform addition, subtraction, multiplication, and division of polynomials, including domain restrictions for division, and master function compositions by evaluating f(g(x)) and substituting g(x) into f.

Divide radicals using the dog operation, pulling out perfect squares and simplifying cube and square roots; rationalize denominators with conjugates for binomial expressions.

Explore how radicals and fractional exponents are two representations of the same idea, and learn to simplify by converting between cube and square roots using exponent rules.

Master solving radical equations by isolating the radical, raising both sides to the appropriate power, and solving resulting linear or quadratic equations, while checking extraneous solutions and noting radical graphs.

Explore graphs of even and odd radical functions, including square and cube roots, with endpoints and turning points. Learn transformations—horizontal and vertical shifts, reflections, and stretches—and end behavior.

Explore inverse relations and functions, using inverse operations and the notation f inverse of x, switch x and y, and apply horizontal and vertical line tests for one-to-one.

Explore graphing inverses by swapping x and y and reflecting the original graph over the line y = x; verify with points and the y = x line.

Explore exponential function graphs, including the parent y = b^x with a horizontal asymptote at y = 0 and the point (0,1). Learn transformations that yield growth and decay.

Apply exponent rules to simplify and rewrite each side with a common base, then equate exponents and solve with algebra. Use product, quotient, and power rules, and handle negative exponents.

Explore how logarithms are the inverse of exponential functions, convert between log and exponential forms, apply the change of base formula using common and natural logs to solve equations.

Explore the properties of logs, including product, quotient, and power rules, and practice condensing and expanding log expressions as the inverse of exponential functions.

Learn natural logarithms and the number e, including its role in compound interest and continuous growth. Apply log rules to convert, condense, expand, and solve equations.

Explore applications of exponential and logarithmic functions, including growth and decay, compound interest, population models, and carbon dating, using e and logs.

Learn to simplify rational expressions and solve multiplying and dividing tasks by factoring, canceling complete factors, and applying keep-change-flip for division.

Learn to add and subtract rational expressions by finding common denominators, combining numerators, and simplifying, with examples including complex fractions and the keep-change-flip.

Explore complex fractions by adding, subtracting, multiplying, and dividing rational expressions, turning them into one fraction over one fraction using keep change flip, with common denominators and exponent rules.

Apply rational expressions to geometry and scenarios, including rectangle perimeter, similar figures, and rectangular-prism surface area. Solve distance-rate-time and work problems, model phosphorus concentration, and use Young's rule for dose.

Graph rational functions by simplifying, locating x-intercepts, vertical asymptotes, horizontal or oblique asymptotes, and holes; determine domain and range, then plot using a step-by-step approach.

Learn to solve rational equations using two methods: convert to a proportion and cross‑multiply, or clear fractions with a common denominator. Check for extraneous solutions to ensure valid results.

Learn direct, indirect (inverse), and joint variation concepts, derive equations y=kx, y=k/x, and y=kxz, and apply to horizon distance, weight, cone volume, and wind force.

Explore conic sections and their standard forms for circles, ellipses, parabolas, and hyperbolas. Use completing the square to convert general form to standard form and uncover centers, radii, and foci.

Explore circles by deriving their equation from a center and radius, using h and k, standard form, completing the square, and graphing with distance and midpoint concepts.

Explore hyperbolas by comparing to ellipses, learn standard forms for horizontal and vertical opens, identify center, vertices, foci, and asymptotes, and practice graphing and deriving equations.

Explore parabolas as a conic section, identifying the vertex, focus, directrix, and p, and use x^2 or y^2 forms to locate axes of symmetry and openings.