P20.1: Demonstrate understanding of the absolute value of real numbers and equations and functions involving the absolute value of linear and quadratic functions.

P20.1.b: Determine the distance of two real numbers of the form ±a, a! R, from 0 on a number line, and relate this to the absolute value of a (|a|).

Rational Numbers, Opposites, and Absolute Values

P20.1.c: Determine the absolute value of a real number.

Rational Numbers, Opposites, and Absolute Values

P20.1.d: Order, with justification, a set of real numbers that includes the absolute value of one or more of the quantities.

Rational Numbers, Opposites, and Absolute Values

P20.1.h: Analyze, describe, and explain the relationship between the graph of y = f(x) and y = |f(x)|.

Absolute Value with Linear Functions
Translating and Scaling Functions

P20.1.k: Develop and apply strategies for determining the intercepts, domain, and range of y = |f(x)| given the equation of the function or its graph.

Absolute Value with Linear Functions

P20.1.l: Explain what the range of the function y = |f(x)| reveals about the graph of the function.

Absolute Value with Linear Functions
Translating and Scaling Functions

P20.1.m: Develop, generalize, explain, and apply strategies for graphically determining (with and without the use of technology) the solution set of an equation involving absolute values of algebraic expressions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

P20.1.n: Develop, generalize, explain, and apply strategies for algebraically determining the solution set of an equation involving absolute values of algebraic expressions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

P20.1.o: Analyze and generalize conclusions about absolute value inequalities of the form |f(x)| < 0.

Absolute Value Equations and Inequalities

P20.1.q: Solve situational questions involving absolute value functions or equations.

Absolute Value with Linear Functions

P20.2: Expand and demonstrate understanding of radicals with numerical and variable radicands including: computations, solving equations (limited to square roots and one or two radicals).

P20.2.a: Develop, generalize, explain, and apply strategies for expressing an entire radical (with numerical or variable radicand) as a mixed radical.

Operations with Radical Expressions
Simplifying Radical Expressions

P20.2.b: Develop, generalize, explain, and apply strategies for expressing a mixed radical (with numerical or variable radicand) as an entire radical.

Operations with Radical Expressions
Simplifying Radical Expressions

P20.2.d: Develop, generalize, explain, and apply strategies for simplifying radical expressions (with numerical and/or variable radicands).

Operations with Radical Expressions
Simplifying Radical Expressions

P20.2.i: Develop, explain, and apply strategies for determining the values of a variable for which a given radical expression is defined.

Radical Functions

P20.2.j: Develop, explain, and apply strategies for determining nonpermissible values (restrictions on values) for the variable in a radical equation.

Operations with Radical Expressions
Radical Functions

P20.2.k: Develop, explain, and apply algebraic strategies for determining and verifying the roots of a radical equation.

Radical Functions

P20.2.l: Explain why some roots determined in solving a radical equation are extraneous.

Operations with Radical Expressions
Radical Functions

P20.4: Expand and demonstrate understanding of the primary trigonometric ratios including the use of reference angles (0° ? ? ? 360°) and the determination of exact values for trigonometric ratios.

P20.4.d: Determine the reference angle for an angle in standard position.

Cosine Function
Sine Function
Tangent Function

P20.4.l: Develop, explain, and apply strategies for solving, for all values of ?, equations of the form sin ? = a or cos ? =a, where ?1 ? a ? 1, and equations of the form tan ? = a, where a is a real number.

Simplifying Trigonometric Expressions
Tangent Function

P20.4.m: Analyze 30°- 60°- 90° and 45°- 45°- 90° triangles to generalize about the relationship between pairs of sides in such triangles in relation to the angles.

Cosine Function
Sine Function
Tangent Function

P20.4.n: Develop, generalize, explain, and apply strategies for determining the exact value of the sine, cosine, or tangent (without the use of technology) of an angle with a reference angle of 30°, 45°, or 60°.

Sum and Difference Identities for Sine and Cosine

P20.4.o: Describe and generalize the relationships and patterns in and among the values of the sine, cosine, and tangent ratios for angles from 0° to 360°.

Cosine Function
Simplifying Trigonometric Expressions
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine

P20.4.p: Create and solve a situational question relevant to one?s self, family, or community which involves a trigonometric ratio.

Sine, Cosine, and Tangent Ratios

P20.6: Expand and demonstrate understanding of factoring polynomial expressions including those of the form: a²x² - b²y², a ? 0, b ? 0; a(f(x))² - b(f(x)) + c, a ? 0; a²(f(x))² - b²(g(y))², a ? 0, b ? 0 where a, b, and c are rational numbers.

P20.6.a: Develop, generalize, explain, and apply strategies for factoring polynomial expressions of the form:

P20.6.a.1: a²x² - b²y², a ? 0, b ? 0, a and b are real numbers

Factoring Special Products

P20.6.a.2: ca²x² - cb²y², a ? 0, b ? 0, a, b, and c are real numbers

Factoring Special Products

P20.6.b: Verify, with explanation, whether or not a given binomial is a factor for a given polynomial.

Quadratics in Factored Form

P20.7: Demonstrate understanding of quadratic functions of the form y = ax² + bx + c and of their graphs, including: vertex, domain and range, direction of opening, axis of symmetry, x- and y-intercepts.

P20.7.d: Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of the function f(x) = a(x-p)² + q without the use of technology.

Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

P20.7.e: Develop, explain, and apply strategies for graphing functions of the form f(x) = a(x - p)² + q by applying transformations related to the values of a, p, and q.

Quadratics in Vertex Form
Translating and Scaling Functions
Translations
Zap It! Game

P20.7.f: Develop, explain, and apply strategies (that do not require graphing or the use of technology) for determining whether a quadratic function will have zero, one, or two x-intercepts.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form

P20.7.h: Develop, generalize, explain, verify, and apply a strategy (including completing the square) for writing a quadratic function in the form y = ax² + bx + c in the form y = a(x - p)² + q.

Parabolas

P20.7.j: Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of a function in the form y = ax² + bx + c.

Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

P20.7.l: Write a quadratic function that models a given situation and explain any assumptions made.

Quadratics in Polynomial Form

P20.7.m: Analyze quadratic functions (with or without the use of technology) to answer situational questions.

Addition and Subtraction of Functions
Quadratics in Polynomial Form

P20.8: Demonstrate understanding of quadratic equations including the solution of: single variable equations, systems of linear-quadratic and quadratic-quadratic equations in two variables.

P20.8.a: Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

P20.8.c: Apply strategies for solving quadratic equations of the form ax² + bx + c = 0 including:

P20.8.c.2: factoring

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

P20.8.c.3: completing the square

Roots of a Quadratic

P20.8.c.4: applying the quadratic formula

Roots of a Quadratic

P20.8.c.5: graphing its corresponding function, with and without the use of technology.

Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

P20.8.e: Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate this knowledge to the number of zeros that the corresponding quadratic function will have.

Roots of a Quadratic

P20.9: Expand and demonstrate understanding of inequalities including: one-variable quadratic inequalities, two-variable linear and quadratic inequalities.

P20.9.a: Develop, generalize, explain, and apply strategies for determining the solution region for two-variable linear or two-variable quadratic inequalities.

Compound Inequalities
Linear Inequalities in Two Variables
Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form)

P20.9.c: Explain, using examples, when a solid or broken line should be used in the graphic solution of a two-variable inequality.

Compound Inequalities
Linear Inequalities in Two Variables
Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form)

P20.9.d: Explain what the solution region for a two-variable inequality means.

Compound Inequalities
Linear Inequalities in Two Variables
Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form)

P20.9.e: Solve a situational question that involves a two-variable inequality.

Compound Inequalities
Linear Inequalities in Two Variables
Systems of Linear Inequalities (Slope-intercept form)

P20.10: Demonstrate understanding of arithmetic and geometric (finite and infinite) sequences and series.

P20.10.a: Identify assumptions made in determining that a sequence or series is either arithmetic or geometric.

Arithmetic and Geometric Sequences

P20.10.c: Provide an example of an arithmetic or geometric sequence that is relevant to one?s self, family, or community.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

P20.10.e: Develop, generalize, explain, and apply a rule and other strategies for determining the values of t?, a, d, n, or tn in situational questions that involve arithmetic sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences

P20.10.f: Develop, generalize, explain, and apply a rule and other strategies for determining the values of t?, a, d, n, or Sn in situational questions that involve arithmetic series.

Arithmetic Sequences

P20.10.g: Solve situational questions that involve arithmetic sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences

P20.10.h: Develop, generalize, explain, and apply a rule and other strategies for determining the values of t?, a, r, n, or tn in situational questions that involve geometric sequences.

Arithmetic and Geometric Sequences
Geometric Sequences