Non-Linear Functions
Students will compare the properties in the family of functions.
Non-linear Functions
In this activity, students graph quadratic functions and study how the constants in the equations compare to the coordinates of the vertices and the axes of symmetry in the graphs. The first part of the activity focuses on the vertex form, while the second part focuses on the standard form. Both activities include opportunities for students to pair up and play a graphing game to test how well they really understand the equations of quadratic functions.
This lesson focuses on having students make connections among different classes of polynomial functions by exploring the graphs of the functions. The questions in the activity sheets allow students to make connections between the x-intercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function. NCTM Publication-Based Lesson Plans are adapted from NCTM's journals. This lesson plan is adapted from an article in the October 2000 edition of Mathematics Teacher Journal.
Students visually model the sequence 2n for n = 1...8 by drawing line segments that represent a tree that doubles its height every year. They then extend the sequence "backward though time" over negative values for n.
Forensics Case 10 - Dropped at the Scene: Blood spatter analysis
In this activity, students graph data to find quantitative relationships and create a standard reference curve for comparison with unknown data. They analyze blood spatters and examine r2 values for linear, natural logarithm, quadratic, and power curve fit. They find the curve that best fits the data and use it to determine the height from which blood has dropped.
In this task, students model a situation with exponential functions in order to make predictions and solve problems.
This activity is designed to give students practice in "finding" the correct factors to use when attempting to factor a trinomial. The students are provided with a Tic-Tac sheet to help them discover the relationship or pattern between two numbers. Students then use their discovery to fill in a second Tic Tac sheet. At this point students have uncovered the mystery of how to locate the appropriate factors in a given trinomial. They can now factor any trinomial placed in front of them!
Teacher & student PDF forms available
Simple unit relating horizontal and vertical speed of falling object
Students compute the initial speed of a falling object using only distance measurements to develop an understanding of quadratic functions. Also provides a simple introduction to composition of functions.
This task asks students to create a pattern using multiple representations (pictures, tables, graphs, and algebraic rules). Students engaged in the task will generate various ways to describe the pattern depending on how they visualize the situation, which will lead to equivalent, but different, expressions.
This task requires students to analyze a situation, describe the appropriate function for the situation using multiple representations, and make connections among the representations. The task provides an opportunity to compare various types of functions.
*linear equations and inequalities *what is an isn't a function
*quadratic functions *parent functions
*connecting word problems to graphs *identifying all of the above visually
This task asks students to analyze and fit a mathematical model to data in order to answer questions about maximizing revenue. Students may use various methods to determine a quadratic function that fits the mathematical model and helps answer the questions.