--- title: "A.FGR.7: Quadratic Functions Modeling (Georgia Mathematics standard)" code: A.FGR.7 cite_as: Georgia Standards of Excellence, Mathematics, A.FGR.7 subject: math grades: - high-school language: en canonical_url: https://georgiahomeroom.org/standards/code/A.FGR.7 md_url: https://georgiahomeroom.org/standards/code/A.FGR.7.md alternate_language_url: https://georgiahomeroom.org/es/standards/code/A.FGR.7.md source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180 source_last_changed: 2024-10-09 data_built: 2026-09-18 publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district. up: https://georgiahomeroom.org/standards/math/high-school.md index: https://georgiahomeroom.org/standards/index.md --- # A.FGR.7: Quadratic Functions Modeling Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. - Subject: Mathematics - Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md ## Expectations - **A.FGR.7.1**: Use function notation to build and evaluate quadratic functions for inputs in their domains and interpret statements that use function notation in terms of a given framework. - **A.FGR.7.2**: Identify the effect on the graph generated by a quadratic function when replacing $f(x)$ with $f(x) + k$, $kf(x)$, $f(kx)$, and $f(x + k)$ for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs. - **A.FGR.7.3**: Graph and analyze the key characteristics of quadratic functions. - **A.FGR.7.4**: Relate the domain and range of a quadratic function to its graph and, where applicable, to the quantitative relationship it describes. - **A.FGR.7.5**: Rewrite a quadratic function representing a mathematically applicable situation to reveal the maximum or minimum value of the function it defines. Explain what the value describes in context. - **A.FGR.7.6**: Create quadratic functions in two variables to represent relationships between quantities; graph quadratic functions on the coordinate axes with labels and scales. - **A.FGR.7.7**: Estimate, calculate, and interpret the average rate of change of a quadratic function and make comparisons to the average rate of change of linear functions. - **A.FGR.7.8**: Write a function defined by a quadratic expression in different but equivalent forms to reveal and explain different properties of the function. - **A.FGR.7.9**: Compare characteristics of two functions each represented in a different way. ## Georgia Milestones coverage - Algebra I (EOC). Functional & Graphical Reasoning. Construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model. (about 12% of the test; 7 points) ## What mastery looks like Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level. - **Beginning**: Evaluate a quadratic function for a given value of the domain. Given the graph of a quadratic function, identify its domain and range. Identify the labels for the axes of a graph of a quadratic function. - **Developing**: Interpret a quadratic function for a given value of the domain in a real-life framework. Given the graph of a quadratic function f(x), identify the graph of f(x) + k, kf(x), f(kx), or f(x + k) for a specified value of k. Given a table of values or graph representing a quadratic function, identify key features of the function. Describe the domain or range of a quadratic function by using formal notation. Identify the maximum or minimum of a function written in vertex form. Identify the graph of a quadratic function. Determine the average rate of change of a quadratic function over a specified interval. - **Proficient**: Create a quadratic function that represents a real-life framework. Explain the result of replacing f(x) in a quadratic function with f(x) + k, kf(x), f(kx), or f(x + k) for a specified value of k. Create the graph of a quadratic function, and identify key features from the graph. Identify and interpret problems involving the domain and/or range of a quadratic function in relation to real-life problems. Rewrite a quadratic function in vertex form to reveal the maximum or minimum and describe that value in context. Create a quadratic function to model a real-life problem. Interpret and compare the average rate of change of a quadratic function and the average rate of change of a linear function over a specified interval. Rewrite quadratic functions to highlight key features in the framework of real-life problems. Compare key features of two different quadratic functions presented in different ways (e.g., tables, equations, graphs). - **Distinguished**: Given a quadratic function represented in a mathematically applicable situation, explain the impact of adjusting the starting value (i.e., f(x) + k), multiplying the output by a constant (i.e., kf(x)), multiplying the input by a constant (i.e., f(kx)), or incorporating a shift (i.e., f(x + k)). Solve real-life problems involving key features of quadratic functions, relating those key features to the mathematically applicable situations. Solve real-life problems involving quadratic functions in various forms by manipulating and comparing the quadratic functions to highlight key features in mathematically applicable situations. Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.