Curriculum  /  Math  /  9th Grade  /  Unit 7: Quadratic Functions and Solutions  /  Lesson 1

Quadratic Functions and Solutions

Lesson 1

Math

Unit 7

9th Grade

Lesson 1 of 13

Objective

Compare quadratic, exponential, and linear functions represented as graphs, tables, and equations.

Common Core Standards

Core Standards

  • F.IF.B.4 — For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • F.LE.A.2 — Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Foundational Standards

  • F.LE.A.1

Criteria for Success

  1. Distinguish between linear, exponential, and quadratic functions in tables, equations, and graphs.
  2. Describe features of quadratic functions represented in graphs.
  3. Describe features of quadratic functions represented in equations.
  4. Describe features of quadratic functions represented in tables, including constant second differences.

Tips for Teachers

The first three lessons in this unit introduce students to features of quadratic functions, as seen in their graphs, tables, and equations. Specifically, they compare and contrast quadratic functions to linear and exponential functions they have studied in previous units.

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Anchor Problems

25-30 minutes

Problem 1

Identify each graph below as an example of a linear function, exponential function, or quadratic function. Use features of the graphs to support your classification.

Guiding Questions

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Problem 2

The three tables below represent a linear function, an exponential function, and a quadratic function. Determine which type of function each table represents and explain your reasoning.

Guiding Questions

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Problem 3

The first three steps of three visual patterns are shown below.

The functions that define the number of tiles in step $$n$$ of each pattern are shown below. Decide which function defines which pattern, and explain your reasoning using the structures seen in the pattern.

$$f(n)=3n^2$$

$$g(n)=n^2+4$$

$$h(n)=n^2-1$$

Guiding Questions

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References

Illustrative Mathematics Quadratic Sequence 1 — Part a

Quadratic Sequence 1, accessed on July 2, 2018, 9:52 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Categorize each representation of a function as linear, exponential, or quadratic. Explain your reasoning for each one.

a.  

$$x$$ $$y$$
1 -2
2 1
3 6
4 13
5 22

 

b.  

$$x$$ $$y$$
1 48
2 24
3 12
4 6
5 3

 

c.      $$f(x)=x(x-4)$$

d.       $$f(x)=4-{x\over2}$$

e.  

f.  

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students analyze, describe, and categorize tables, equations, and graphs as linear, exponential, or quadratic
  • Approximately Normal Experiences in Math Perplexed in Patterns — (This is a great activity to follow Anchor Problem #3 and to engage students in investigating quadratic patterns)
  • Illustrative Mathematics Identifying Functions — (Students may have seen an adapted version of this task in Unit 6)
  • Mathematics Vision Project: Secondary Mathematics Two Module 1: Quadratic Functions — Lesson 1.1 "Go"

Next

Identify key features of a quadratic function represented graphically. Graph a quadratic function from a table of values.

Lesson 2
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Factoring and Solutions of Quadratic Equations

Topic C: Interpreting Solutions of Quadratic Functions in Context

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