Exploring Polynomials—Quadratics

Teacher copy

This lab is designed to be used in tandem with teaching quadratic equation graphing. There are many topics and concepts to discuss here, like axis of symmetry and vertex; but it is up to the instructor to decide how “deep” they want to go.

Personally, I have found it quite difficult for students to understand this topic. First, I would show students how to graph y=x^2 and y=3x^2 ….(via table and graph paper.) Second, I would work on both horizontal and vertical shifts; however, I would do them using both the TI-83 and graphing paper. Personally, I feel that this use of technology only enhances the students understanding of the topic at hand. Finally, the main focus of the lab would be to have the students apply there understanding of parabolic shapes to experiments using the CBR. A suggestion would be to have them produce the plot of a bouncing ball. Then have them “fit” an equation into one of the parabolic curves (they would need to understand vertex, concavity…) Also, you could have them write quadratic equations of graphs that you put up on the overhead using the TI-83. The possibilities of this lab aren’t exhausted here, but it sure is a good start.

Furthermore, you could introduce or enrich the students knowledge of roots, points of intersection (using 2 different graphs), other calculator functions like maximum and minimum. Again the possibilities you can use here not exhausted.

Exploring Polynomials ---Quadratics

Student copy

Objective:

This lab is designed to teach you about quadratic equation terminology and graphing. You will be using the TI-83, the CBR, bouncing balls and other things to complete this lab. We are treating this lab as an introduction to quadratics. So, don’t be too afraid just yet.

First, the teacher is going to introduce terminology and general ideas to you. Use the space and graph paper provided.

Second, we are going to work on horizontal and vertical shifts. More room and graph paper are provided. Are you getting the idea?? If not, you had better ask!!

Now, here comes the main part of the lab. Your teacher is going to elaborate on this particular portion of the lab. You are going to be using the CBR and the TI-83. You will be applying the concepts you have learned thus far in quadratics.

Some questions to answer: (your teacher will probably add to this list)

1) Explain in your own words the following: roots, vertex, points of intersection, quadratic shifts

2) What is the general equation of a parabola? What exactly do the coefficients represent?

3) Do you notice a “pattern” to aid in graphing parabolas using pencil and paper?