Non – Linear Equations Quadratic Equations

1. Non – Linear EquationsQuadratic Equations Sarah Grant

2. Unit Questions • What is the difference between Linear and Non Linear Equations? • What is the Quadratic Equation and what is it used for? • How do you use models, tables, graphs, and algebraic methods to solve? • How does a constant change the graph of an equation?

3. Activities • Internet Projects • Exploring quadratic equations – Learn it Teach it : http://edu.learnit-teachit.org/lessons/Math/Exploring_Quadratic_Equations/ • Quadratic equations in projectile motion problems - Inquiry Leading to Understanding : http://www.my-ecoach.com/online/teacherguide4.php?projectid=233 • Software Applications

4. Objective Through this unit the students will come to understand the differences between equation types; linear, quadratic and other non linear equations. By using functions the students will learn how to interpret and represent data – and the relationships between that data - and to model and represent solutions to a problem.

5. Blooms Taxonomy • Knowledge • Comprehension • Application • Learn about quadratic and other non linear equations • Be able to complete problems using the information • Apply knowledge in real world scenarios • Understand differences between linear and non linear equations

6. TEKS • § 111.32. Algebra I (a)  Basic understandings. (3)  Function concepts. A function is a fundamental mathematical concept; it expresses a special kind of relationship between two quantities. Students use functions to determine one quantity from another, to represent and model problem situations, and to analyze and interpret relationships. (b) Knowledge and skills. (9)  Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to: (A)  determine the domain and range for quadratic functions in given situations; (B)  investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c; (C)  investigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c; and (D)  analyze graphs of quadratic functions and draw conclusions.

7. TEKS (cont) (10)  Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to: (A)  solve quadratic equations using concrete models, tables, graphs, and algebraic methods; and (B)  make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. • §126.26. Multimedia (c)  Knowledge and skills. (8)  Solving problems. The student uses research skills and electronic communication, with appropriate supervision, to create new knowledge. The student is expected to: (A)  participate with electronic communities as a learner, initiator, contributor, and teacher/mentor and use technology to participate in self-directed and practical activities in the larger community and society;

8. Resources Texas Education Agency. (2010 Nov 17). Mathematics – High School. Retrieved on 2011 Feb 7 from http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html Texas Education Agency. (1998 Sept 1). Technology Applications – High School. Retrieved on 2011 Feb 14 from http://ritter.tea.state.tx.us/rules/tac/chapter126/ch126c.html