Public learning track
Coordinate Intersections, Graphical Solutions, and Equivalence
9th Grade · Math · Open Global Math
8 lessons
Goal
Explain graphs as solution sets, find intersection coordinates of y = f(x) and y = g(x) to solve f(x) = g(x), and compare growth models.
Featured Diagrams
Graphs as Complete Solution Sets in the Coordinate Plane
8 lessons
0 of 8 done
- 1Graphs as Complete Solution Sets in the Coordinate PlaneUp nextStart
- 2Solving Equations Graphically Using IntersectionsPremiumNot started yet
- 3Approximating Solutions to Equations GraphicallyNot started yet
- 4Identifying Linear Growth from GraphsNot started yet
- 5Identifying Exponential Growth from GraphsNot started yet
- 6Identifying Growth Type from EquationsNot started yet
- 7Observing That Exponential Growth Eventually Exceeds Linear Growth from GraphsNot started yet
- 8Observing That Exponential Growth Eventually Exceeds Quadratic Growth from GraphsNot started yet
Standards Covered
- OGM.10.FNC.8Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, and explain why the x-coordinates of the intersection points of y = f(x) and y = g(x) are the solutions to f(x) = g(x).
- OGM.10.FNC.2Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Analyze, graph, and write linear functions in slope-intercept, point-slope, and standard forms; determine slope, rate of change, parallel and perpendicular slopes, and x- and y-intercepts; and model direct variation.
- OGM.10.FNC.4Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Model exponential growth and decay situations, graph exponential and logarithmic functions (bases 2, 10, e), identify key features (intercepts, asymptotes), convert between exponential and logarithmic forms, and solve exponential and logarithmic equations.
- OGM.10.FNC.3Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Graph and analyze quadratic functions in standard, vertex, and factored forms; identify key attributes (vertex, axis of symmetry, intercepts, extrema); convert between forms; and formulate quadratic models from points or data.
Curriculum Framework
9th Grade · Math · Open Global Math
1
11 lessons
Functions, Domain, Range, and Piecewise Representations
Evaluate functions, determine domain and range across multiple notations, and construct and analyze piecewise-defined functions.
2
17 lessons
Linear Functions, Forms, Slopes, and Direct Variation
Analyze, graph, convert, and model with linear functions in all forms, including slope relationships and direct variation.
3
9 lessons
Quadratic Functions, Forms, and Key Attributes
Analyze, convert, graph, and model quadratic functions across standard, vertex, and factored forms.
4
11 lessons
Exponential and Logarithmic Functions, Graphs, and Equations
Model growth and decay, graph exponential and logarithmic functions across bases 2, 10, and e, and solve equations.
5
8 lessons
Parent Function Families and Inverse Variation
Graph and analyze parent functions (absolute value, square root, cube root, reciprocal, cubic, sine/cosine) and model inverse variation.
6
7 lessons
Transformations of Parent Functions
Apply, identify, and formulate vertical and horizontal translations, stretches, compressions, and reflections across all function families.
7
7 lessons
Inverse Functions, Composition, and Invertibility
Determine inverse functions algebraically, verify inverses via composition and graphical symmetry, and restrict domains for one-to-one invertibility.
8
9 lessons
Arithmetic and Geometric Sequences and Series
Represent arithmetic and geometric sequences recursively and explicitly, link to linear/exponential growth, and derive and evaluate geometric series.
9
8 lessons
Coordinate Intersections, Graphical Solutions, and Equivalence
Explain graphs as solution sets, find intersection coordinates of y = f(x) and y = g(x) to solve f(x) = g(x), and compare growth models.