F-IF.7:  Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior.

Students understand set builder notation for the graph of a real-valued function: {(x, f(x)) | x ∈ D}.
Students learn techniques for graphing functions and relate the domain of a function to its graph.

Students understand the meaning of the graph of y = f(x), namely {(x,y) | x ∈ D and y = f(x)}.
Students understand the definitions of when a function is increasing or decreasing.

Students graph simple quadratic equations of the form y = a(x - h)2 + k (completed-square or vertex form), recognizing that (h,k) represents the vertex of the graph and use a graph to construct a quadratic equation in vertex form.
Students understand the relationship between the leading coefficient of a quadratic function and its concavity and slope and recognize that an infinite number of quadratic functions share the same vertex.

Students compare the basic quadratic (parent) function, y = x2, to the square root function and do the same with cubic and cube root functions. They then sketch graphs of square root and cube root functions, taking into consideration any constraints on the domain and range.

Students create a quadratic function from a data set based on a contextual situation, sketch its graph, and interpret both the function and the graph in context. They answer questions and make predictions related to the data, the quadratic function, and graph.

From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for functions addressed in previous modules (i.e., linear, exponential, quadratic, cubic, square root, cube root, absolute value, and other piecewise functions).

Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.

Students explore quadratic functions by using a motion detector known as a Calculator Based Ranger (CBR) to examine the heights of the different bounces of a ball. Students will represent each bounce with a quadratic function of the form y = a (x - h)^2 + k. This lesson plan is based on the activity Tremain Nelson uses in the video for Part II of this workshop.

Students will research types of bridges, identify symmetry and types of functions and use linear functions to design a bridge.

Students will be able to have a better understanding of the slope of a line, the y intercept, and parallel lines.

This lesson is an exploration focusing on the symmetric nature of quadratic functions and their graphs and the interpretation of the key features.

Class activity with scenario where students have to write and evaluate exponential function.

This lesson unit is intended to help teachers assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to: find, from their equations, lines that are parallel and perpendicular; and identify and use intercepts. It also aims to encourage discussion on some common misconceptions about equations of lines.

The purpose of the task is to build fluency with the procedural work of linear and exponential functions. This task is designed to help students recognize the information given in a problem and use it efficiently. In the task, students will work with both linear and exponential functions given in tables, graphs, equations, and story contexts. They will construct various representations, with an emphasis on writing equations using various forms and using equations to graph the functions.

The purpose of this task is to compare the rates of growth of an exponential and a linear function.
The task provides an opportunity to look at the growth of an exponential and a linear function for
large values of x, showing that increasing exponential functions become much larger as x increases.
This task is a good opportunity to model functions using technological tools and to discuss how to
set appropriate viewing windows for functions. The task also leads to a discussion of whether this
particular situation should be modeled using discrete or continuous functions.

In this Khan Academy activity, students will graph a parabola given any form,

In this Khan Academy activity, students will graph a parabola given its factored form.