between rational and irrational numbers. They consider quadratic function, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students learn that when quadratic equations do not have real solutions the number system must be extended so that a solution exists, analogous to the way in which extending the whole numbers to the negative numbers allows X+1=0 to have a solution. Formal work with complex numbers comes in Algebra II. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise defined. The eight lessons (5.1-5.8) provide the instruction and practice that supports the culminating activity in the final unit project. The lessons in this unit focus on working with quadratic relationships.

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In this lesson students will learn why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational and that the product of a nonzero rational number and in irrational number is irrational. Students will address how rational numbers and irrational numbers are alike and how they are different. For example, we use the ? in the formula for the area of a circle and the ? in the formula of an ellipse as an example of an irrational number. In this lesson we will calculate the area of a typical putting green on a golf course and the area of a track field, which is in the shape of an ellipse.
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In this lesson students discover parabolas in real life and create parabolas on graphs. Students learn about quadratic functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Students will relate the domain of a function to its graph and when applicable, to the quantitative relationship it describes.
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Lesson 5.3: Quadratic Functions and Rate of Change
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In this lesson, students continue to work on their graphing skills, by hand in simple cases and using technology for more complicated cases, to identify key features including intercepts, maxima, and minima. Graphs will include linear, quadratic, square root, cube root, and piecewise-defined functions, and possibly step functions and absolute value functions. The focus will be on identifying the type of function by comparing the graphical representations.
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When factoring a polynomial is not possible students will use the technique of completing the square to solving quadratic equations. Using this process of factoring and completing the square in a quadratic function, students will show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
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In this lesson, students will learn about quadratic functions that model a relationship between two quantities. They will apply this function to graphing.
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In this lessons students will learn to build new functions from existing functions and find inverse functions.
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In this lesson students learn to construct and compare linear, quadratic, and exponential models and solve problems. They will compare linear and exponential growth to quadratic growth. Students will observe using graphs and tables that a quantity increase exponentially eventually exceeds a quantity increasing as a linear, quadratic, or polynomial function.
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In this project students will graph quadratic functions based on the popular game, Angry Birds, by using equations and a Web-based graphing tool. Students will work in groups to apply the same principles to create their own game that uses quadratic functions. Students will exchange games with other groups, play the game and assess that game using a set student rating scale.
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