Lesson+Plan+4+(1pg+2)

Lesson 4 Algebra 3-4 Section 4.1 (pt 1) Date: 24 November 2008 Learning Experience: //Introduction// – Today the class will begin its move from working with linear functions to quadratic functions. The class will warm-up with the idea of transformations of the standard // y // =//x// graph and describing in words what happens to it through the alterations of the following graphs: // y // =3//x// // y // =//x// – 2 // y // = 5//x// + 1 // y // =| //x// – 1| // y // =2 |//x//| // y // = |//x// + 1| - 2 //Discovery activity/Questions// – ·  How can we change the starting point of a linear graph or an absolute value graph? ·  When I add a number to a standard linear graph, what are two different ways to describe its alteration? //Class work// – If the 400 LAB is available the class will move to that room and use the computers to run a simulation on http://phet.colorado.edu/sims/equation-grapher/equation-grapher_en.html to learn and write rules for the development of alterations of the quadratic equations as found in their text. A worksheet for this scenario is attached. If the room is not available the class will learn the materials in a more traditional manner. The following materials need to be covered. A __ quadratic function __ is a function that can be written in the standard form of //y = ax//2 + //bx// + //c// where //a// ≠ 0. The graph of this function is called a __ parabola __. The graph of this function has a point that is an extreme value (either maximum or minimum). This point is called the __ vertex __. Where is the vertex of the basic //y// = //x^//2 graph? Through the vertex there is an imaginary line that would act as a mirror. Everything on either side of this line is an exact mirror image of the other side. The line is called a __ line of symmetry __. Look at the graphs of the following equations and find the vertex and the axis of symmetry: //y// = //x^//2 //y// = //x^//2 + 1 //y// = 3//x^//2 + 2 //y// = //x^//2 + //x// //y// = //x^//2 – //x// //y// = //x^//2 – 2//x// + 1 How do the vertex and the axis of symmetry relate? In all of the proceeding examples how can we find the //y//-intercept? What would happen to the extrema if the //x//2 term would have been negative? How can we generalize this rule? //Homework// – Page 240 #12 – 15, 19, 20, 21 – 26.

NOTE: I was able to secure a computer lab for this lesson. The students completed the worksheet at this link: [|Lesson 4 Worksheet.pdf].