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· Throughout this course, you will represent equations and functions in several different ways, and you will make connections between the various representations.
· How can these connections help you understand more about systems of equations? In this lesson, you will make connections among the multiple representations of a system ofequations.
· 1-63.An action movie is being filmed at the Perrine Bridge in Twin Falls, Idaho. The hero of the movie, Wynono Homer, leaps off the bridge over the Snake River and then pulls a parachute to slow his fall. To avoid risk, the director will use computer-generated imagery (CGI) for this scene. The animators must create an accurate model of the jump and descent to make the scene look realistic!
· Before he pulls the parachute, Wynono’s path can be modeled by the equation
h=–4.9t2+t+148. The height above the Snake River is represented byh(meters), andt(seconds) is the amount of time of his jump.
· The movie director gives the animators the following table, which shows the approximate heights and times the director wants Wynono to pass through after he opens his parachute.
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· According to this information, at what height will Wynono open his parachute in the movie scene?
· Your Task:Work with your team to findas many ways as you can(withandwithout your graphing calculator) to determine the height above the river at which Wynono opens his parachute. Be sure to analyze tables, graphs, and equations as you work. What is an appropriate domain for each of the functions that describe Wynono’s descent?
How can we use graphs?
How can we use tables?
How can we use equations?
· 1-64.In this lesson, you used several methods to locate a point of intersection of two functions.
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1. Work with your team to determine the points of intersection of the functionsf(x) = 2x2– 5x+ 6 andg(x) = –2x2–x+ 30. Demonstrate as many methods as you can, both with and without your graphing calculator.
2. Can you find a way to make the graphing calculator calculate the points of intersection for you? How accurate are your results? Be prepared to share your method with the class.
0. 1-65.LEARNING LOG
0. In your Learning Log, explain how the points of intersection of graphs of functions can be determined (or verified) using the multiple representations of a system of equations. Provide examples and a sketch. Title this entry “Determining Points of Intersection” and include today’s date.
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Laws of Exponents
In the expressionx3,xis the base and 3 is the exponent. Here are the laws of exponents with examples: