2/14/22 Assignment - Complete 5.1.5 + 2-page Learning Log/Report on Quadratic Representations Today, we will continue to work on what is referred to in CPM as the "Quadratic Web." This is the web diagram that highlights connections between all of the different ways that we can see a quadratic function represented: 1) Equation (including x-squared and often, but not always, an x term and a constant term) 2) Table 3) Graph (parabola, which may go on infinitely, but could also be restricted in domain/range) 4) Situation (word problem scenario describing a relationship between two variables that would graph as a parabola, commonly with domain and range restrictions, like the water balloon toss, which had a specific launching and landing point and only included the parabola section in between) Lesson 5.1.5, COMPLETING THE QUADRATIC REPRESENTATIONS WEB If you did not do so previously, begin by completing problems 5-49 thru 5-51 with your team, and then follow the instructions for writing a multiple page Learning Log about different ways of representing Quadratic equations/functions (see below): A) Classwork problems: Complete team problems 5-49 (must include rough graph sketch and matching equation, not just letters/numbers), 5-50, and 5-51 B) Multi-Page Learning Log (individual writing, but collaborate with your team, as this will prepare everyone for a team challenge): You will complete a "Quadratic Representations" Learning Log (a written math journal entry), addressing the following: 1) PART 1: FOUR REPRESENTATIONS & THEIR CHARACTERISTICS: List each of the four quadratic representations (table, graph, equation, situations, as described above) with an explanation of the most important characteristics or features of each (can be bullet points). In other words, how would you look at each "representation" and know it is representing a quadratic function, or what features would you expect it to have or patterns would you expect it to follow given that it is quadratic? It may be helpful to contrast it with linear or exponential in terms of the graph, patterns in its tables, and the form of the equation. 2) PART 2: CONVERTING BETWEEN AND CONNECTING THE REPRESENTATIONS: Describe how to do each of the following processes, using a specific problem or equation or table to graph to illustrate (these can be examples from your completed CPM problems that you simple re-write or put pictures of into your learning log, and then describe alongside those example problems): a) Using an Equation to Create a Table (of x, y coordinates) and a Graph (as we did in lesson 5.1.2) b) Changing the Standard Form of a quadratic equation to the Factored Form of the equation, and using the solutions to graph x-intercepts and to find and graph the vertex of the parabola (as we did in lessons 5.1.3/5.1.4) c) Taking data from a Table (with x-intercepts) and using it to work backwards and write factors and then multiply them back to the full quadratic equation, including testing an additional point to identify any potential common number factors or a negative that needs to be multiplied thru (as we did in lesson 5.1.4) d) Reading a described situation, like that of the water balloon toss competition, and identifying critical points for graphing [like intercepts and vertex or domain and range restrictions] or for completing a table (as we did in Lesson 5.1.2) Your Learning Log can be done digitally or by hand, or some combination. When you are including graphs, if doing it digitally, you can create the graphs in DESMOS and insert screenshots or hand draw graphs and insert pictures of those graphs at some point. If you use DESMOS and there is a restricted domain and/or range, you should try to find a way to specify that when you create your graph (e.g., for the water balloon toss, the graph should not really go on indefinitely, since the water balloon can no go below ground). You can decide individually what works best for you in terms of handwriting versus digital, even though you may be discussing and collaborating on putting the Learning Log entry together/coming up with the main points to be addressed or written about. Your Learning Log is a summary of everything you have learned across four full lessons, so it is reasonable to expect it to be at 2+ full pages in length, more like a report than a more simple journal entry. This will be your first step in getting ready for your next major team challenge, which is to create a Representations Web for a quadratic, system of linear, and exponential functions.