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.
?
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
F.IF.C.7.A
F.IF.C.8.A
G.GPE.A.2
Identify features of quadratic functions from equations and use these features to graph quadratic functions. Derive the equation of a parabola.
F.IF.C.7.A
F.IF.C.8.A
Identify the y-intercept and vertex of a quadratic function written in standard form through inspection and finding the axis of symmetry. Graph quadratic equations on the graphing calculator.
A.SSE.A.2
A.SSE.B.3.A
F.IF.C.8.A
Write a quadratic equation in intercept form by factoring. Describe the features of a quadratic function written in intercept form.
F.IF.B.4
F.IF.C.9
F.BF.B.3
Transform a quadratic function in vertex form. Describe the domain, range, and intervals where the function is increasing and decreasing.
A.REI.A.1
A.REI.B.4.B
Solve quadratic equations written in vertex form and describe graphical features from vertex form.
A.SSE.B.3.B
A.REI.B.4.B
Complete the square to convert an equation written in standard form to an equation written in vertex form.
N.CN.A.1
N.CN.C.7
A.REI.B.4.B
Identify solutions that are non-real from a graph and an equation using the discriminant. Define imaginary and complex numbers.
N.CN.A.1
N.CN.A.2
Add, subtract, and multiply complex numbers.
F.IF.B.6
F.IF.C.8.A
F.IF.C.9
F.BF.A.1
F.BF.B.3
Compare, analyze, and solve quadratic functions in projectile motion application problems.
F.IF.B.6
F.IF.C.8.A
F.IF.C.9
F.BF.A.1
Describe features of quadratic functions in the context of a word problem. Evaluate and use function notation to describe contextual situations.
A.REI.A.1
A.REI.C.7
A.REI.D.11
Identify solutions to a system of a quadratic function and a linear function graphically and algebraically.
Key: Major Cluster Supporting Cluster Additional Cluster
?
?