Download Algebra 2 Ch. 2 CCSS (Common Core State Standards) A

Algebra 2
Ch. 2
CCSS (Common Core State Standards)
A-SSE Seeing Structure in Expressions
Interpret the structure of expressions
1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
2. Use the structure of an expression to identify ways to rewrite it.
A-APR Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials
1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction,
and multiplication; add, subtract, and multiply polynomials.
F-IF Interpreting Functions
Interpret functions that arise in applications in terms of the context
4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and
sketch graphs showing key features given a verbal description of
the relationship.
Analyze functions using different representations
7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Analyze functions using different representations
9. Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions).
F-BF Building Functions
Build a function that models a relationship between two quantities
1. Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations.
Build new functions from existing functions
3. Identify the effect on the graph of replacing f(x) by f(x) 1 k, k f(x), f(kx), and f(x 1 k) for specific values of k (both positive and negative);
find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and algebraic expressions for them.
A-CED Creating Equations
Create equations that describe numbers or relationships
1. Create equations and inequalities in one variable and use them to solve problems
N–CN The Complex Number System
Perform arithmetic operations with complex numbers.
1. Know there is a complex number i such that i2 5 21, and every complex number has the form a 1 bi with a and b real.
2. Use the relation i2 5 21 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
3. (1) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Understand the relationship between zeros and factors of polynomials
3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined
by the polynomial.
Use complex numbers in polynomial identities and equations.
7. Solve quadratic equations with real coefficients that have complex solutions.
8. (1) Extend polynomial identities to the complex numbers.
9. (1) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Learning Goals
As the chapter moves along, evaluate yourself using the Shamrock Learning Scale.
2.1

_____ I can match a quadratic function with its corresponding graph.

_____ I can identify key characteristics of quadratic functions based on the form of the function.

_____ I can analyze the different forms of quadratic functions.

_____ I can use key characteristics of specific forms of quadratic functions to write equations.

_____ I can write quadratic functions to represent problem situations.

_____ I can analyze the basic form of a quadratic function.

_____ I can identify the reference points of the basic form of a quadratic function.

_____ I can understand the structure of the basic quadratic function.

_____ I can graph quadratic functions through transformations.

_____ I can identify the effect on a graph by replacing f(x) by f(x -C) + D.

_____ I can identify transformations given equations of quadratic functions.

_____ I can write quadratic functions given a graph.

_____ I can graph quadratic functions through vertical dilations.

_____ I can identify the effect on a graph by replacing f(x) by Af(x).

_____ I can write quadratic functions given a graph.

_____ I can graph quadratic functions through horizontal dilations.

_____ I can identify the effect on a graph by replacing f(x) by f(Bx).

_____ I can write quadratic functions given a graph.

_____ I can determine how many points are necessary to create a unique quadratic equation.

_____ I can derive a quadratic equation given a variety of information using reference points.

_____ I can derive a quadratic equation given three points using a system of equations.

_____ I can derive a quadratic equation given three points using a graphing calculator to perform a quadratic
2.2
2.3
2.4
2.5
regression.
2.6

_____ I can calculate powers of i.

_____ I can interpret the real numbers as part of the complex number system.

_____ I can add, subtract, and multiply complex numbers.

_____ I can add, subtract, and multiply complex polynomial expressions.

_____ I can understand that the product of complex conjugates is a real number.

_____ I can rewrite quotients of complex numbers.

_____ I can determine the number and type of zeros of a quadratic function.

_____ I can solve quadratic equations with complex solutions.

_____ I can use the Fundamental Theorem of Algebra.
2.7

_____ I can choose an appropriate method to

_____ I can determine zeros of quadratic functions.