Activity 1 [IS.5 - Struggling Learners] [IS.6 - All Students]
The path of a fighter jet is represented by the function h = –15m²+ 60,000. Sketch the graph of the path of the jet and answer the following questions:
1. What is the approximate height after 28 minutes? 54 minutes?
2. How many minutes does it take for the jet to reach an altitude of 46,000 feet?
3. What is the vertex, and what does it mean in the context of the problem?
4. If another fighter jet, represented by the function h = –17m²+ 56,000, sets out at the same time for the same destination, which fighter jet will make the quickest trip? Why?
5. What is the domain and range of each jet path? Explain the meaning in everyday terms, relating it directly to the context of the problem.
A tennis ball is thrown into a trash can. Draw the path of the ball, from the moment it leaves the thrower’s hands. On the graph, representing the path of the ball, label and describe each part of the process, as time continues. Provide information, regarding the vertex, domain, and range. Describe and explain in terms of the problem. What are the x-and y-intercepts? What do they mean in the context of the problem? [IS.7 - All Students]
Students will compare graphs and discuss possible reasons for differences and similarities. Students should discuss the idea of rate of change with quadratic functions. What kind of rate of change do we have here? (Encourage students to use an actual tennis ball to investigate the function.)
Divide students into groups of three to four. Create two real-world scenarios of quadratic functions; model with tables and graphs; and pose and answer at least three appropriate questions for each. Create one problem from the science realm and one from the business arena. Create a visual to present to the class. [IS.8 - All Students]
Monique states that a person traveling down a slide represents a parabolic function. Determine if you concur or dissent. Provide supporting evidence, including representations, examples, and explanations. [IS.9 - All Students]
Activity 5: Performance
Divide students into groups of three or four. Students will create an animated PowerPoint presentation with a twofold purpose. Purpose 1 is to illustrate transformations of functions. Transformations should be supported and explained by audio, while animation is used to show the different transformed functions. Purpose 2 is to illustrate a real-world quadratic function in action. The PowerPoint will pose a problem; simulate a real-world occurrence; represent the function in equation, tabular, and graphical forms; and pose and respond to three or four questions. [IS.10 - Struggling Learners] [IS.11 - All Students]
· Have students provide examples of related absolute value and quadratic functions. Students should illustrate each with appropriate representations, while explaining the reasons behind the choice in function for each example. In other words, why was an absolute value function used to model this piece of the example? Could we use a quadratic function? If we used a quadratic function, what would change regarding our interpretations? (and vice versa) Encourage students to delve deep into their understanding of connections of absolute value functions and quadratic functions with the real world. The intent is to see if they can make connections between the two types of functions, thus exhibiting a very high level of conceptual understanding related to these ideas.