Features of Quadratic Functions (Lesson 7.4)
Unit 1: Generalizing Patterns
Day 1: Intro to Unit 1
Day 2: Equations that Describe Patterns
Day 3: Describing Arithmetic Patterns
Day 4: Making Use of Structure
Day 5: Review 1.1-1.3
Day 6: Quiz 1.1 to 1.3
Day 7: Writing Explicit Rules for Patterns
Day 8: Patterns and Equivalent Expressions
Day 9: Describing Geometric Patterns
Day 10: Connecting Patterns Across Multiple Representations
Day 11: Review 1.4-1.7
Day 12: Quiz 1.4 to 1.7
Day 13: Unit 1 Review
Day 14: Unit 1 Test
Unit 2: Linear Relationships
Day 1: Proportional Reasoning
Day 2: Proportional Relationships in the Coordinate Plane
Day 3: Slope of a Line
Day 4: Linear Equations
Day 5: Review 2.1-2.4
Day 6: Quiz 2.1 to 2.4
Day 7: Graphing Lines
Day 8: Linear Reasoning
Day 9: Horizontal and Vertical Lines
Day 10: Standard Form of a Line
Day 11: Review 2.5-2.8
Day 12: Quiz 2.5 to 2.8
Day 13: Unit 2 Review
Day 14: Unit 2 Test
Unit 3: Solving Linear Equations and Inequalities
Day 1: Intro to Unit 3
Day 2: Exploring Equivalence
Day 3: Representing and Solving Linear Problems
Day 4: Solving Linear Equations by Balancing
Day 5: Reasoning with Linear Equations
Day 6: Solving Equations Using Inverse Operations
Day 7: Review 3.1-3.5
Day 8: Quiz 3.1 to 3.5
Day 9: Representing Scenarios with Inequalities
Day 10: Solutions to 1-Variable Inequalities
Day 11: Reasoning with Inequalities
Day 12: Writing and Solving Inequalities
Day 13: Review 3.6-3.9
Day 14: Quiz 3.6 to 3.9
Day 15: Unit 3 Review
Day 16: Unit 3 Test
Unit 4: Systems of Linear Equations and Inequalities
Day 1: Intro to Unit 4
Day 2: Interpreting Linear Systems in Context
Day 3: Interpreting Solutions to a Linear System Graphically
Day 4: Substitution
Day 5: Review 4.1- 4.3
Day 6: Quiz 4.1 to 4.3
Day 7: Solving Linear Systems Using Elimination
Day 8: Determining Number of Solutions Algebraically
Day 9: Graphing Linear Inequalities in Two Variables
Day 10: Writing and Solving Systems of Linear Inequalities
Day 11: Review 4.4- 4.7
Day 12: Quiz 4.4 to 4.7
Day 13: Unit 4 Review
Day 14: Unit 4 Test
Unit 5: Functions
Day 1: Using and Interpreting Function Notation
Day 2: Concept of a Function
Day 3: Functions in Multiple Representations
Day 4: Interpreting Graphs of Functions
Day 5: Review 5.1-5.4
Day 6: Quiz 5.1 to 5.4
Day 7: From Sequences to Functions
Day 8: Linear Functions
Day 9: Piecewise Functions
Day 10: Average Rate of Change
Day 11: Review 5.5-5.8
Day 12: Quiz 5.5 to 5.8
Day 13: Unit 5 Review
Day 14: Unit 5 Test
Unit 6: Working with Nonlinear Functions
Day 1: Nonlinear Growth
Day 2: Step Functions
Day 3: Absolute Value Functions
Day 4: Solving an Absolute Value Function
Day 5: Review 6.1-6.4
Day 6: Quiz 6.1 to 6.4
Day 7: Exponent Rules
Day 8: Power Functions
Day 9: Square Root and Root Functions
Day 10: Radicals and Rational Exponents
Day 11: Solving Equations
Day 12: Review 6.5-6.9
Day 13: Quiz 6.5 to 6.9
Day 14: Unit 6 Review
Day 15: Unit 6 Test
Unit 7: Quadratic Functions
Day 1: Quadratic Growth
Day 2: The Parent Function
Day 3: Transforming Quadratic Functions
Day 4: Features of Quadratic Functions
Day 5: Forms of Quadratic Functions
Day 6: Review 7.1-7.5
Day 7: Quiz 7.1 to 7.5
Day 8: Writing Quadratics in Factored Form
Day 9: Solving Quadratics using the Zero Product Property
Day 10: Solving Quadratics Using Symmetry
Day 11: Review 7.6-7.8
Day 12: Quiz 7.6 to 7.8
Day 13: Quadratic Models
Day 14: Unit 7 Review
Day 15: Unit 7 Test
Unit 8: Exponential Functions
Day 1: Geometric Sequences: From Recursive to Explicit
Day 2: Exponential Functions
Day 3: Graphs of the Parent Exponential Functions
Day 4: Transformations of Exponential Functions
Day 5: Review 8.1-8.4
Day 6: Quiz 8.1 to 8.4
Day 7: Working with Exponential Functions
Day 8: Interpreting Models for Exponential Growth and Decay
Day 9: Constructing Exponential Models
Day 10: Rational Exponents in Context
Day 11: Review 8.5-8.8
Day 12: Quiz 8.5 to 8.8
Day 13: Unit 8 Review
Day 14: Unit 8 Test
Learning Targets
Identify a relationship between the vertex and the x-intercepts of a quadratic function using symmetry.
Use graphs, tables, and equations to identify the vertex, intercepts, and other values of a quadratic function.
Determine if a parabola opens up or down.
Tasks/Activity | Time |
---|---|
Activity | 20 minutes |
Debrief Activity with Margin Notes | 10 minutes |
QuickNotes | 5 minutes |
Check Your Understanding | 15 minutes |
Activity: Parabola Patterns
Lesson Handouts
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Answer Key
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Homework
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Experience First
Today’s lesson builds on what students know about the symmetry of parabolas to determine key features of quadratics, specifically the location of the x-intercepts of the function. For questions 1-3, students are given the full graph of the parabola and must determine the axis of symmetry and the x-intercepts. In question 2, students notice that there are two solutions to some quadratic equations and that these solutions must be equidistant from the axis of symmetry. Knowing this will help students tackle question 3, where students must again reason about the horizontal distance between a point on the parabola and the axis of symmetry. Finally, in question 4 students are given two points on a new parabola and must use symmetry to find additional points. Monitoring Questions:
Formalize Later
A large emphasis is placed on symmetry in this lesson because it sets the stage for an upcoming lesson on solving quadratic equations. We like approaching quadratics in this way because symmetry is generally intuitive for students and allows them to make sense of solutions visually, instead of just relying on algebraic procedures. Even without a graph, students should be able to identify that points equidistant from the axis of symmetry will have the same output. In question 2 of the CYU, students are given a quadratic represented as a table. Students should still be able to use symmetry to reason about values on the parabola. One strategy for reasoning with tables is to find two x-values where the output is the same, and then locate the axis of symmetry by finding the point half-way between the two x-values. While this question uses consecutive x-values, students should be prepared for cases where the inputs increase by uneven amounts.