Algebra 2 (& GT)
Unit 2: Expanding Understanding of Quadratic Functions
What will my child learn?
Students will:
Analyze functions using different representations. (From Algebra I)
F.IF.C.8
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function (SAT® Content  PAM.01  PAM.09) (Review from Algebra I)
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
Perform arithmetic operations with complex numbers.
N.CN.A.1
Know there is a complex number i such that i^2 = 1, and every complex number has the form a + bi with a and b real (SAT® Content  ATM.01).
N.CN.A.2
Use the relation i^2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Solve equations and inequalities in one variable.
A.REI.B.4
Solve quadratic equations in one variable (SAT® Content  PAM.02).
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form (SAT® Content  PAM.02).
Use complex numbers in polynomial identities and equations.
N.CN.C.7
Solve quadratic equations with real coefficients that have complex solutions.
Solve Systems of Equations.
A.REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically (SAT® Content  PAM.03).
Use complex numbers in polynomial identities and equations.
N.CN.C.9 (+)
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. (Algebra II GT only)
N.CN.C.8 (+)
Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). (Algebra II GT only)
Use coordinates to prove simple geometric theorems algebraically.
G.GPE.A.2
Derive the equation of a parabola given a focus and directrix. (Algebra II GT only)
Students will:
Analyze functions using different representations. (From Algebra I)
F.IF.C.8
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function (SAT® Content  PAM.01  PAM.09) (Review from Algebra I)
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
 Check for Understanding: Key Features of Quadratic Functions
 Review/Rewind: Forms and Features of Quadratic Functions
 Enrichment Tasks: Which Function?  Springboard Dive
Perform arithmetic operations with complex numbers.
N.CN.A.1
Know there is a complex number i such that i^2 = 1, and every complex number has the form a + bi with a and b real (SAT® Content  ATM.01).
 Review/Rewind: What Are Complex Numbers?
 Enrichment Tasks: Complex Number and Patterns  Vertex of a Parabola with Complex Roots
N.CN.A.2
Use the relation i^2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
 Review/Rewind: Adding Complex Numbers  Multiplying Complex Numbers
 Enrichment Tasks: Powers of a Complex Number  Complex Square Roots
Solve equations and inequalities in one variable.
A.REI.B.4
Solve quadratic equations in one variable (SAT® Content  PAM.02).
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form (SAT® Content  PAM.02).
 Review/Rewind: Rewriting Quadratics as Perfect Squares
 Review/Rewind: Solving Quadratic Equations by Square Root  Solving Quadratic Equations by Factoring  Solving Quadratic Equations by Completing the Square  Solving Quadratic Equations Using the Quadratic Formula
 Enrichment Tasks: Two Squares are Equal  Vertex of a Parabola with Complex Roots
Use complex numbers in polynomial identities and equations.
N.CN.C.7
Solve quadratic equations with real coefficients that have complex solutions.
 Review/Rewind: Solving Quadratic Equations with Complex Roots
 Enrichment Tasks: Completing the Square
Solve Systems of Equations.
A.REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically (SAT® Content  PAM.03).
 Enrichment Tasks: Pythagorean Triples  A Linear and Quadratic System
Use complex numbers in polynomial identities and equations.
N.CN.C.9 (+)
Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. (Algebra II GT only)
 Review/Rewind: Quadratics and the Fundamental Theorem of Algebra
N.CN.C.8 (+)
Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). (Algebra II GT only)
 Review/Rewind: Complex Numbers and Sum of Squares Factorization
Use coordinates to prove simple geometric theorems algebraically.
G.GPE.A.2
Derive the equation of a parabola given a focus and directrix. (Algebra II GT only)
 Review/Rewind: Equation of a Parabola from a Focus and Directrix
 Enrichment Tasks: Defining Parabolas Geometrically
What are some signs of student mastery?
Graphical Analysis and Modeling of Quadratic Functions

Tools & Technology
Desmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! Practice adding complex numbers with the Complex Adding Maze. 