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Math · Algebra 1 · Unit 7

Unit 7: Introduction to Quadratic Functions

Students look at patterns that grow quadratically, contrast quadratic growth with linear and exponential growth, and examine standard, factored, and vertex forms of quadratic functions.

Worksheets

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Unit
📝 Worksheet ✅ Answer guide
Concept
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Practice
Set 1
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Set 2
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Advanced
Set 1
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Set 2
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What this unit covers

A A Different Kind of Change · 2 lessons
Goals
  • Comprehend that a “quadratic relationship” can be expressed with a squared term.
  • Determine and explain whether a visual pattern represents a linear, exponential, or quadratic relationship.
Lessons
  1. A Different Kind of Change
  2. How Does It Change?
B Quadratic Functions · 5 lessons
Goals
  • Interpret quadratic functions that represent a physical phenomenon, given expressions and graphs.
  • Use graphs, tables, and calculations to show that exponential functions eventually overtake quadratic functions.
Lessons
  1. Building Quadratic Functions from Geometric Patterns
  2. Comparing Quadratic and Exponential Functions
  3. Building Quadratic Functions to Describe Situations (Part 1)
  4. Building Quadratic Functions to Describe Situations (Part 2)
  5. Building Quadratic Functions to Describe Situations (Part 3)
C Working with Quadratic Expressions · 3 lessons
Goals
  • Coordinate a quadratic expression given in factored form and the intercepts of its graph.
  • Use the distributive property to write equivalent quadratic expressions from factored into standard form.
Lessons
  1. Equivalent Quadratic Expressions
  2. Standard Form and Factored Form
  3. Graphs of Functions in Standard and Factored Forms
D Features of Graphs of Quadratic Functions · 7 lessons
Goals
  • Explain how a graph is affected by changing parameters in quadratic expressions written in standard, factored, and vertex forms.
  • Use an equation in vertex form to identify the maximum or minimum of a quadratic function.
Lessons
  1. Graphing from the Factored Form
  2. Graphing the Standard Form (Part 1)
  3. Graphing the Standard Form (Part 2) (Optional)
  4. Graphs That Represent Situations (Optional)
  5. Vertex Form
  6. Graphing from the Vertex Form (Optional)
  7. Changing the Vertex
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Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.