Algebra 2 - The Complete Course 2025

Explore the coordinate system on the x-y plane, use Cartesian coordinates to locate points, and compute distance and midpoint.

Plot points on the x y plane and interpret coordinates as ordered pairs, identifying each point’s address by its x and y components and moving from the origin.

calculate the length of a line segment between two points on the coordinate plane using the distance formula, the square root of (x2 - x1)^2 + (y2 - y1)^2.

Apply the distance formula to compute the length between two points, and simplify results such as sqrt(25)=5 and sqrt(50)=5 sqrt(2).

Apply the distance formula to find the length of the line segment between A(-1,5) and B(3,9), simplifying sqrt(32) to 4 sqrt(2).

Apply the midpoint formula to find the midpoint of a line segment by averaging the x coordinates and the y coordinates of endpoints A and B.

apply the midpoint formula to find the line segment midpoint by averaging x coordinates and y coordinates, illustrated with endpoints a and b.

Learn to compute the length of a line segment between two points using the distance formula and find the midpoint by averaging the coordinates.

Derive the standard equation of a straight line, y = 2 m x + C, and explore the slope m and y-intercept C, plus x- and y-intercepts and linearity.

Explore slope or gradient concepts with positive, negative, and zero cases on a straight line. Learn to compute the exact gradient using the two-point formula and keep point order consistent.

Derive the equation of a straight line through points (2,5) and (0.5,2) by computing the slope m=2 and y-intercept c=1, yielding y=2x+1.

Find the equation of a straight line from two points using slope and intercept, with points (0,2) and (6,-2), yielding y = -2/3 x + 2.

Explore methods for equations of a straight line: test points by substitution and construct lines from slope and a point, including horizontal lines, using y = m x + c.

Solve and verify straight-line equations by practicing five exercises: passing through points, using the gradient, testing which points lie on the line, and deriving slope-intercept forms.

Learn to determine slope and y intercept from standard and nonstandard line equations by rearranging to y = mx + c.

Master the point-slope form y - y1 = m(x - x1) for a straight line, and compute slope from two points to obtain y = mx + c.

Practice solving straight-line equations from gradient and points, using the slope-intercept form y = mx + c and substitution, including cases with two points.

Examine two straight-line forms: y = m x + c and y − y1 = m(x − x1); learn slope as (y2 − y1)/(x2 − x1) from points.

Explore the standard equation of a straight line, y = m x + c, identifying the slope m and y-intercept c, and see how these constants define a line's position.

Learn how to find the intersection of two lines by solving their equations simultaneously, then substitute to obtain the point of intersection, such as (2, -3) for the example.

Sketch each line by plotting points for y = 4x and y = -3x + 7, then solve them simultaneously to find their intersection at (1, 4).

Practice six exercises on intersections of two lines, graph sketching, and the distance formula, reinforcing straight-line concepts and sharpening problem-solving skills in Algebra 2.

Explore how the y-intercept affects the elevation of parallel lines by plotting three lines with equal slope but different intercepts, and connecting points to visualize their differences.

Explore how identical y intercepts with different slopes produce lines of varying steepness by plotting points and comparing angles; higher slopes yield steeper lines while the intercept stays the same.

Explore how parallel lines have equal slopes and never intersect, and how perpendicular lines have slopes that are negative reciprocals, with the product of slopes equal to minus one.

Explore solving for lines parallel or perpendicular to a given line that pass through a specified point, using slope relationships and intercept calculations to derive the equations.

Practice exercises on parallel and perpendicular lines through points (2,3) and (1,2), using rearrangement to standard form to find slopes; first solution yields y equals minus two x plus one.

Explore how line slopes relate to parallel and perpendicular relationships, using gradient equalities and negative reciprocals. Find intersection points by solving the two line equations simultaneously.

Explore how a function acts as a box mapping each input to a unique output, using f(x)=2x-1, and see the resulting straight-line graph with x horizontal and f(x) vertical.

Explore common function graphs, from straight lines to parabolas, cubics, square roots, absolute value, and exponential and trigonometric graphs. Learn why the circle x^2+y^2=1 is not a function.

Understand the straight line equation y = m x + c, identify the y-intercept and slope, and see how changing c shifts the line while equal slopes produce parallel lines.

Explore functions as one-to-one input-output rules where input yields a single output. Visualize function f(x)=3x-1 on a graph with x as the independent variable and y as the dependent variable.

Learn to test if a graph is a function by checking mappings: parabola y = x^2 and y = x^3 are functions; x = y^2 and circle are not.

Explore fundamental functions and their graphs, including constant, identity, linear, square, quadratic, cubic, square root function, and reciprocal functions, and observe their key features for future lessons.

Examine vertical and horizontal asymptotes using graph y = 1/x, showing how x = 0 is excluded and the graph approaches infinity near zero and zero as x grows large.

Explore how graphs reveal limits: as x approaches zero from either side, f(x) tends to infinity or negative infinity, and as x grows without bound, f(x) tends to zero.

Practice memorizing and reproducing the functions and graphs discussed so far, preparing you to recognize and apply them as they recur throughout algebra 2.

Explore translations in algebra by shifting graphs vertically; learn how adding or subtracting a constant to f(x)=2x^2 moves the parabola up or down without changing its shape.

Explore horizontal shifts of a parabola by replacing x with x-2 to shift right by 2 and with x+4 to shift left by 4, relative to the original y=x^2.

Explore graph translations by typing f(x) expressions on an interactive site to observe how adding or subtracting constants shift parabolas and cubes vertically and horizontally.

Explore vertical shifts up or down and horizontal shifts right or left in graphs of f(x) created by adding or subtracting constants or replacing x with x−h or x+h.

Explore how vertical and horizontal translations move the parabola y = x^2, then combine them to see the translated graph and its new center.

Explore transformations of graphs by stretching and compressing: apply vertical stretch y=2f(x) to increase height, and horizontal compression y=f(3x) to shorten the cycle.

Participate in a shark activity on graph sketch dot com to explore transformations of f(x)=2x^3, comparing before- and after-exponent multiplications, with adjustable x and y ranges.

Practice transforming a piecewise linear graph by applying f(2x) for horizontal compression and 2f(x) for vertical stretching, describing how the domain and range change.

Explore vertical stretches and compressions by multiplying the function's output by a positive constant, then apply horizontal changes with f(ax), where a>1 compresses and 0<a<1 stretches.

Explore translations and transformations of graphs, including vertical shifts up or down and horizontal shifts right or left, plus vertical and horizontal scaling with a, yielding compression or stretch.

Explore reflections of graphs about the x-axis and y-axis. Learn how multiplying the output or the input by -1 transforms parabolas and square root graphs, altering turning points and positions.

Explore reflections of graphs: y = -f(x) reflects about the x-axis, while y = f(-x) reflects about the y-axis.

Apply translations, reflections, and transformations to sketch complex graphs from simple ones, using the inverse and square root graphs as templates and practicing step-by-step exercises.

Master translating, transforming, and reflecting basic functions to sketch graphs; memorize constant, linear, quadratic, cubic, square root, and reciprocal functions; apply limits to describe behavior, intercepts, and turning points.

Memorize and recognize common graphs such as linear, parabola, cubic, square root, absolute value, reciprocal, circle, natural log, exponential, cosine, sine, and tangent, and apply transformations to build new graphs.

Explore six types of graph manipulations, focusing on translations: shift up by a in y=f(x)+a and shift in x via x + a or x - a.

Explore reflection of graphs across the x-axis and y-axis using f, -f, and f(-x). Learn y-direction stretching by a and x-direction squeezing by 1/a, with zeros fixed.

Learn how a parabola is manipulated through stretching, reflections, and translations, using y = x^2, y = 5x^2, and y = 2x^2 + 3.

Explore exploratory data analysis and descriptive statistics with categorical and quantitative data using frequency distributions, bar charts, pie charts, pareto diagrams, dot plots, histograms, cross tabulation, simpson's paradox.

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