Students build on their knowledge of the features, forms, and representations of quadratic functions, and extend their understanding from solutions in the real number system to the complex number system.
In Unit 2, Quadratics, students review the features, forms, and representations of quadratic functions and extend their understanding from the solutions in the real number system to the complex number system. In this unit, students will also deepen their understanding of solutions of systems of quadratic equations and applications modeled with quadratic functions.
Unit 2 begins with students identifying features of quadratic functions in multiple representations and converting between representations to reveal features, including transformations and symmetry, and connections between factoring and completing the square. Next in this unit, students will determine the number and kind of solutions using the discriminant, using graphical analysis, and by identifying non-real solutions found algebraically. Students will operate with complex numbers in Topic B as well, drawing connections to properties of operations in the real number system. In Topic C, students will extend the kinds of situations that can be modeled with quadratic functions from projectile motion, studied in Algebra 1, to geometric and profit function applications. Finally, students will review and extend their understanding of systems of quadratic equations; in the advanced course students will also explore systems with circles. If the advanced course is being taught, students will also investigate conjugates of complex numbers, write imaginary roots in intercept form, and restrict the domain of quadratics to render them invertible.
As students continue their work in Algebra 2, analysis, transformations, systems, and inverse of functions and other equations will continue to be a theme. As more functions are added to the student repertoire, students will be expected to draw upon multiple understandings to solve problems.
Pacing: 13 instructional days (11 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Unit-Specific Intellectual Prep
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roots, intercept, maximum, minimum, vertex | standard, vertex, intercept (factored) form | leading coefficient | perfect square trinomial |
double root | difference of two squares | equation of a circle: $${x^2+y^2=r^2}$$ | invertible function |
real and non-real solutions | imaginary numbers | complex numbers | discriminant |
complex roots | tangent line | inverse functions | domain restriction |
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Use [Y=] and [GRAPH] to graph
Use [WINDOW] to adjust the viewing window
Use [Zoom] "0. ZoomFit"
Use [Zoom] "6. ZoomStandard"
Use [CALC] and [TRACE] functions
Key: Major Cluster Supporting Cluster Additional Cluster
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