A.FGR.7Quadratic Functions Modeling

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.