Introduction Math problems often require many steps and involve using many rules that you have learned both here in this course and in your past encounters with math. Completing the Problem of the Week and detailing each step in words will enhance your understanding of the concepts and help me pinpoint any areas that you may need additional help. As you complete each step, write a sentence or two that explains what you did and which algebraic rules or principles you applied. Note: The Week 3 Problem of the Week document will need to be uploaded into both the Moodle dropbox and the Taskstream Assignment dropbox. Activity Instructions Quadratic equations can be used to represent real-world phenomena such as the arced path of a tossed ball, supply and demand analysis, and area maximization problems. Sometimes seeing a graph of the equation can help to fully understand what is happening with a function. The graph and the equation can give us clues necessary to put the pieces together. After you finish answering the math questions related to the function below, you will have to think about how the process of using clues to find information could be useful to you in other areas of your life. Use the function f (x)=2(x+3)2-4 to answer the following questions. Make sure you use the Chapter 3 Problem of the Week document to record your answers. a. What is the type of shape described by the function called? Explain your reasoning. b. Find the zeros (or x-intercepts) of the function. Explain all steps involved. c. Find all y-intercepts of the function and explain all steps involved. Sketch a graph of the function. You may draw it on your own paper, take a picture, then add it to the document or sketch it on the grid below. a. Using the appropriate interval form, over which interval(s) is the graph increasing? b. Using the appropriate interval form, over which interval(s) is the graph decreasing? c. Using the appropriate interval form, what is the domain of the function? Explain the reasoning for your answer. d. Using the appropriate interval form, what is the range of the function? Explain the reasoning for your answer. As you can see from your work above, one small equation can contain many pieces of information. You just have to have to know where to look and the skills to extract the secrets it contains. Explain how you can use this process of looking for clues in the evidence presented to solve a problem in your future career.
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