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$f(x) = \frac{10}{22}x-71$

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The Discriminant and Parabolas

Exploring End Behavior of Polynomials

Cubics and Points of Inflection

Solving Exponential Equations by Graphing

Solving Rational Equations by Graphing

Exploring Asymptopes

CO2 Creating Teaching Materials

Algebra I Honors with Geogebra

School Board of Broward County Adopted Text:

McDougal Littell’s Algebra 1 Equations, Graphs, and Applications

Long Term Topic: Library of Functions

The Library of Functions (Linear, Absolute Value, Polynomial, Exponential, Rational, and Radical Functions) provides teachers and students with a bridge between the real number system and the real world. In Algebra I Honors, students evaluate expressions and solve equations using each member of the library listed above. Moreover, teachers and students graphically represent these functions to aid in the modeling, analysis, and solving of both real world and mathematical problems.

As students progress through the library, the concept of a parent function and transformations on that parent function for each member is explored graphically using Geogebra. Students are asked to consider all quadratics in general through a beginning parent function, and as the need arises, transform that parent function to fit a particular mathematical or real world situations. It is through these graphical representations that students and teachers will develop a deeper understanding of the connections between algebra, geometry, and the real world. In future courses, the library is built upon as more functions are introduced and explored.

The following marked sections from the chapters below either directly lend themselves to the Library of Function concept, or they provide direct pathways from concepts in Algebra to concepts in Geometry, and could therefore be efficiently investigated using Geogebra.

Chapter 1: Connections to Algebra

• 1.1-1.2 Evaluating Variable Expressions (GR)
• 1.3 Powers
• 1.5 Equations and Inequalities (GR)
• 1.7 Introduction to Functions
• A) Domain / Range
• B) Linear/ Quadratic (Triangular Numbers)

Chapter 2: Properties of Real Numbers

• 2.1 Absolute Value

Chapter 3: Solving Linear Equations

• 3.2 Solving Equations with Multiplication + Division (Similar Triangles)
• 3.5 Linear Equations and Problem Solving (Cheetah)
• 3.7 Formulas and Functions (Inverse Functions)

Chapter 4: Graphing Linear Functions and Equations

• 4.1 Coordinates and Scatter Plots
• 4.2 Graphing Linear Equations
• 4.3 Quick Graphs using Intercepts
• 4.4 Slope
• 4.5 Direct Variation
• 4.6 Quick Graphs Using Slope-Intercept Form
• 4.7 Solving Linear Equations Using Graphs
• 4.8 Functions and Relations

Chapter 5: Writing Linear Equations

• 5.1 Writing Linear Equations
• 5.2 Writing Linear Equations Given a Point and a Slope
• 5.3 Writing Linear Equations Given 2 Points
• 5.4 Best Fitting Line
• 5.5 Writing Linear Equations Given 2 Points
• 5.6 The Standard Form of a Line
• 5.7 Predicting with Linear Models

Chapter 6: Solving and Graphing Linear Inequalities

• 6.3 Solving Compound Inequalities (Triangle Inequalities)
• 6.4 Solving Absolute Value Equations and Inequalities
• 6.5 Graphing Linear Inequalities in Two Variables

Chapter 7: Systems of Linear Equations and Inequalities

• 7.1 Solving Linear Systems by Graphing
• 7.4 Applications of Linear Systems
• 7.5 Special Types of Linear Systems
• 7.6 Solving Systems of Linear Inequalities

Chapter 8: Exponents and Exponential Functions

• 8.2 Zero and Negative Exponents (Exponential Functions)
• 8.5 Exponential Growth Functions
• 8.6 Exponential Decay Functions

Chapter 9: Quadratic Equations and Functions

• 9.4 Solving Quadratic Equations by Graphing
• 9.5 Quadratic Equations (Vertical Motion)
• 9.6 Applications of the Discriminant
• 9.8 Comparing Linear, Exponential, and Quadratic Models (Pendulum)

Chapter 10: Polynomials and Factoring

• 10.1-10.3 Operations on Polynomials (Polynomial Functions)
• 10.4 Solving Polynomial Equations in Factored Form
• 10.5 - 10.7 Factoring Quadratics
• 10.8 Factoring Using the Distributive (Volume of a Box)

Chapter 11: Rational Equations and Functions

• 11.1 Ratio and Proportion (Scaling)
• 11.3 Direct and Inverse Variation (Bicycle Banking Angle)
• 11.8 Rational Equations and Functions (Asymptotes)

Chapter 12: Radicals and Connections to Geometry

• 12.1 Functions Involving Square Roots