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.
Math
Unit 2
11th Grade
In Unit 2, 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, 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)
The following assessments accompany Unit 2.
Use the resources below to assess student understanding of the unit content and action plan for future units.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Unit-Specific Intellectual Prep
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 |
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
Topic A: Features of Quadratic Functions
Topic B: Imaginary Solutions and Operating with Complex Numbers
Topic C: Applications, Systems, and Inverse with Quadratics
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Next
Identify features of quadratic functions from equations and use these features to graph quadratic functions. Derive the equation of a parabola.
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