Algebra 1 - A Complete Course

Master solving multi-step equations by combining like terms and isolating the variable using the coefficient. Apply distributive property in practice problems, including shirt and bumper sticker costs, and verify solutions.

Learn to solve equations with variables on both sides by moving terms across the equals sign, combining like terms, and verifying the solution by substitution.

Solve proportions using cross-multiplication, the butterfly method, and proportional reasoning, with checks to verify solutions across fractions and real-world examples.

Identify similar figures, establish corresponding sides, and use proportions to determine unknown measurements across maps and scale models, including calculating map scales and real-world distances.

Explore solving multi-step inequalities and related word problems through review exercises, including variable setup and solving for x in age and budgeting scenarios.

See how the number of rectangles relates to the perimeter through a linear function, with perimeter = 2x + 12, and extend the idea to triangles and pattern-based equations.

Explore patterns and nonlinear functions by analyzing x–y changes, identifying linear versus nonlinear relationships, and examining examples like x^3 and the circumference as a function of radius.

Graph linear functions using slope-intercept form, identify slope and y-intercept, and plot points with rise over run. Apply to a weight-capacity example to build a five-point graph.

Distinguish continuous versus discrete graphs and model scenarios with functions. Identify independent and dependent variables, using 16 ounces per gallon of cheddar to relate gallons, ounces, and money.

Graphing a function rule (review) covers slope concepts, identifying discrete functions, and sketching graphs of parabolas and cubic curves by plotting key points.

Explore writing a function rule that links outdoor temperature to cricket chirps, and apply function models to landfill waste growth, concert revenue, and a rectangle's area.

Explore domain and range for relations and functions, illustrate with mapping diagrams and the vertical line test, and identify function status by x-value uniqueness.

Explains rate of change as the slope of a linear relation, using a marching band to show 260 feet per minute and change in y over change in x.

Explore rate of change and slope through real-world examples like miles per gallon, mph, and newspaper delivery, teaching how to compute slope from coordinates and time.

Identify direct variation using y = kx, determine k as y/x, and verify the origin intercept; apply the concept to examples such as weight on Earth and Mars.

Learn to express lines in slope-intercept form y = mx + b, identify slope m and y-intercept b, and apply rise-over-run to graph and model costs.

Explore standard form, Ax + By = C, learn to find x- and y-intercepts, convert to slope-intercept form, determine the slope, including vertical lines when B is zero.

Explore transformations of linear functions, including vertical and horizontal translations, reflections across the x- and y-axes, and both inside and outside scaling that changes slope.

This lecture reviews solving systems by substitution, isolating a variable and substituting into the other equation, including no solution and infinite solutions with t-shirts and pants price problems.

This lesson demonstrates solving linear systems by substitution or elimination and by graphing to find break-even where income equals expenses, using y = 5.5x + 700 and y = 12.5x.

Test points in linear inequalities and distinguish them from equations. Graph the solution region above or below the boundary line, using solid or dashed lines to indicate inclusion.

Master zero and negative exponents by applying a^0 = 1 and a^(-n) = 1/a^n, and simplify expressions with negative powers while exploring a doubling growth model.

Master zero and negative exponents by simplifying fractions and expressing expressions as one over terms, including powers.

Explore rational exponents and radicals, convert between radical and exponential forms, and simplify expressions like 64 = 4^3 and 27^(2/3) = 9.

Explore simplifying radicals by factoring inside the radicand to extract square factors, combine factors to form squares, and rationalize denominators, with multiple worked examples.

Explore geometric sequences using the recursive formula, determine the first term and common ratio, and compute subsequent terms through the recurrence.

Explore how to classify polynomials by degree and terms, from monomials to binomials and trinomials, and learn to add or subtract them by combining like terms in standard form.

Master adding and subtracting polynomials by combining like terms, arranging terms from highest to lowest degree, and recognizing monomials, trinomial structures, and polynomial degrees.

Explore how to multiply binomials using distribution, work through binomial–trinomial products, and consolidate results by combining like terms for clear polynomial expansion.

Learn to factor ax^2 + bx + c by extracting a common factor, splitting the middle term, and factoring by grouping to obtain a product of binomials.

Review factoring by grouping to factor expressions with multiple terms, identify common factors, and apply grouping techniques to simplify polynomials.

Learn to simplify rational expressions by factoring and canceling common factors, and identify restrictions or excluded values that keep denominators nonzero.

Learn how to divide polynomials using long division, identify the dividend and divisor, and obtain the quotient and remainder with clear step-by-step rules.

Analyze how the coefficient a stretches or compresses and vertical shifts affect quadratic graphs, then apply to a downward opening acorn height model, determining domain and range.

Explore quadratic graphs and their properties, identify the vertex and axis of symmetry, determine maximum or minimum values, and relate domain and range to graph transformations.

learn to determine the axis of symmetry x = -b/(2a) and the vertex, then graph quadratics using symmetry and three symmetric points including the y-intercept.

Explore quadratic functions by locating the vertex and axis of symmetry, using x = -b/(2a). Apply to a projectile height model to find maximum height and time to hit ground.

Learn how to transform quadratic functions with vertical and horizontal reflections, stretches, compressions, and translations, distinguish inside (input) versus outside (output) changes, and apply the proper transformation order.

The lecture reviews transformations of quadratic functions, emphasizing horizontal shifts from x minus h, vertical translations, and the standard form y = a(x-h)^2 + k with focus on rightward moves.

Review quadratic equations by factoring, identify roots, and transform between forms, including writing quadratics in vertex form and verifying with standard form.

Explore the quadratic formula and the discriminant to solve quadratics, learning when D>0 yields two real solutions, D=0 one, and D<0 none, with factoring, completing the square, or graphing.

Identify exponential functions from data points, examine their domain and range, and apply an exponential model such as 15000(1.06)^t to project costs rising over time.