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
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?
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
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
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
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)
 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
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. 