Objective-- Quadratic Functions (7-8 weeks)

[Scope and Sequence]
[Foundations For Functions][Parameter Changes][Linear][Quad Functions][Square Root Functions][Rational Functions][Exponential & Logarithmic][Conics]

This unit includes equations, inequalities, and systems. There should be an emphasis on the connection between the 5 representations: graph, table, problem situation, pictorial, symbolic. Within this unit, connections to foundations for functions and how all functions have same traits should be made.
Quadratic Functions (7-8 weeks)
Objective	TEKS	TEKS Clarification	TAKS Objective	SATEC Lesson/Resource(s)	SATEC Correlated Assessment	Dana Center Assessments	Resources/Text
Identify and sketch the quadratic function	2A.4A	Revisit data activity from Foundations for Functions and reinforce common function characteristics. Revisit data to extend the investigation of quadratic functions to include writing equations, graphing and translating functions, and analyzing parameter changes in the context of situations; look at the roots, solutions, and zeroes and connect them to x-intercepts, discuss concavity, min/max, and from this write a function rule when given the vertex and a point. Solve quadratic equations using the most efficient algebraic method (factoring and quadratic formula) Emphasize the connection to between min/max & domain/range. Discuss the relationship of min/max with respect to concavity. Add, subtract, & multiply complex numbers for the purpose of determining a quadratic function from its roots. Write quadratic functions from roots, a graph, tables, or by completing the square. Determine the independent and dependent variables and analyze the possible domain and range values appropriate for the given situation. Use technology such as graphing calculators and/or computers to link multiple representations	Obj 1: Alg I A.1A, A.1B, A.1C, A.1D, A.1E Obj 2: Alg I A.2A, A.2B, A.2C, A.2D, A.3A, A.3B, A.4A, A.4B Obj 5: Alg I A.9B, A.9C, A.9D, A.11A Alg II 2A.7A, 2A.7B	Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)		Introduction to Quadratics
Describe limitations of domain and range of quadratic functions	2A.6A			Over Da Watta!	Over Da Watta!-- (Reflect and Apply)
Recognize a situation that can be modeled by a quadratic function and relate representations of quadratic functions.	2A.6B			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)
Sketch the parent quadratic function, investigate, describe and predict the effects of parameter changes in applied and mathematical situations	2A.7B 2A.4B			Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply) Changing Lots		Algebra II Institute Part I: 1.1, 2.1 Algebra II Institute Part A: II 1.1
Use the method of completing the square to write a quadratic function in the form y= a(x-h)² +k.	2A.5E
Connect between the two forms of a quadratic function. y= ax² +bx +c and y= a(x-h)² +k.	2A.7A			Introduction to Quadratics Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)	Sink Hole!
Analyze situations and formulate quadratic equations or inequalities to model the problem.	2A.8A			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)	Fixed Area Fixed Perimeter
Analyze the possible domain and range values for a quadratic function and for a problem situation	2A.6A 2A.1A			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)	Comparing Volumes
Solve quadratic equations and inequalities using algebraic methods (factoring and quadratic formula) and technology	2A.8B 2A.8D			Math In The Shadows	Math In The Shadows--(Reflect and Apply) Exploring the Discriminant	Triangle Problem. Motion Under Gravity. Toricelli's law
Compare and translate between algebraic and graphical solutions to quadratic equations.	2A.8C			Over Da Watta!	Over Da Watta!-- (Reflect and Apply) Changing Lots Exploring the Discriminant	Doing What Mathematicians Do. Parabolic Path.
Use complex numbers to describe the roots of a quadratic equation.	2A.2B				Exploring the Discriminant
Determine a quadratic function from its roots or its graph.	2A.6C			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)		Introduction to Quadratics
For a given application, identify the mathematical domain and range and the domain and range for the situation.	2A.1A			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)
Collect and organize data , make scatterplots, fit the curve to a function, interpret the results, and model, predict, and make decisions.	2A.1B			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)
Recognize that functions can be denoted in many forms: y =, d =, y=, and f(x) = and determine which form is the most appropriate for a given situation.	2A.2C
Perceive functions and equations as means for analyzing and understanding relationships and as tools for expressing generalizations.	BU A3						Introduction to Quadratics
Use a variety of representations, tools, and technology and model situations to solve problems.	BU A5			Over Da Watta!	Over Da Watta!-- (Reflect and Apply) Changing Lots
Use math processes throughout, including problem solving, computation, communication, connections, reasoning, multiple representations, modeling, and justification	BU A6			Over Da Watta! Math In The Shadows	Over Da Watta!-- (Reflect and Apply) Math In The Shadows--(Reflect and Apply)

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