IA2.AT.D: Model with functions.

Model with functions.

IA2.AT.D.11Write a quadratic function to model relationships between quantities given a narrative description, table of values, or graph.IA2.AT.D.12Represent and interpret quadratic functions using tables and graphs and apply them in context. a. Create tables and graphs to represent quadratic relationships and identify key features. Key features include: intercepts/zeros, symmetry, intervals of increase and decrease, relative extrema, end behavior, domain (if restricted in context), and range. b. Relate key features in the table and graph to characteristics of a context. c. Justify the appropriateness of a quadratic model by analyzing trends in the table or graph and explaining how the model’s features support predictions or contextual interpretations.IA2.AT.D.13Find and interpret the inverse of quadratic and exponential functions using algebraic and graphical representations. a. Restrict the domain of a quadratic to make it one-to-one and express its inverse as a square root function. b. Express the inverse of an exponential function as a logarithmic function and evaluate expressions involving logarithms. c. Graph a function and its inverse and analyze features (e.g., domain and range, intercepts, points of intersection) and symmetry across the line y = x. d. Interpret the meaning of inverse functions in context.IA2.AT.D.14Represent and interpret higher degree polynomial (degree 3 or higher), and radical functions in context using tables and graphs. a. Create tables and graphs to represent higher degree polynomial functions and identify key features. Key features include: intercepts/zeros, symmetry, intervals of increase and decrease, relative extrema, and end behavior. b. Create tables and graphs to represent radical functions and identify key features. Key features include: domain restrictions, intercepts, intervals of increase and decrease, and end behavior. c. Relate key features of higher-degree polynomial and radical functions to contexts.IA2.AT.D.15Analyze how transformations affect the graph of a polynomial function given in vertex form and interpret their meaning in context. a. Identify how the graph of a quadratic function changes when f(x) is replaced by f(x + k), f(x) + k, and kf(x) and determine the value of k from the graph. Describe the type of transformation. b. Explain the meaning of each transformation by connecting the structure of the transformed function to the quantities it represents (e.g., how changes affect the vertex, direction of opening, and rate of change).

1-on-1 AI tutoring aligned to IA2.AT.D. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →