Lesson 2 | Quadratic Functions and Solutions | 9th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Interpreting Functions

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.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.

Interpreting Functions

F.IF.C.7.A — Graph linear and quadratic functions and show intercepts, maxima, and minima.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Use vocabulary to describe the features of graphs of parabolas, including maximum, minimum, line of symmetry, $${y-}$$intercept, roots/solutions/$${x-}$$intercepts, facing up/down, domain and range.
Annotate parabolas with features.
Sketch a graph of a quadratic function given particular features.
Graph a quadratic function using a table of values.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Describe each graph below and find a reason why each one does not belong with the other three graphs.

Guiding Questions

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References

Which One Doesn't Belong Graph 6

Problem 2

Sketch a quadratic function that meets the following requirements:

has a vertex that is a maximum
has two roots, one that is positive and one that is negative
is increasing over the interval $${-\infty < x < 2}$$
is decreasing over the interval $${2<x<\infty}$$

Guiding Questions

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Problem 3

Graph the following quadratic equations by creating a table of values. Annotate each graph.

$${f(x)=-2x^2+3}$$

$${g(x)=(x-3)(x+2)}$$

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Graph the quadratic function below by creating a table of values. Annotate the graph with features of the function.

$${j(x)=2x^2-6x+4}$$

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.

Have students write descriptions of parabolas and then swap with a peer to then graph the parabola from the written description

Desmos Polygraph: Parabolas — (Could be done on computers or adapted to be done on paper)
EngageNY Mathematics Algebra I > Module 4 > Topic A > Lesson 8 — Problem Set
Kuta Software Free Algebra 1 Worksheets Graphing Quadratic Functions — (Have students create a table of values to graph each function)

Lesson 1

Lesson 3

Lesson Map

Topic A: Features of Quadratic Functions

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

F.IF.B.4 F.LE.A.2

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

F.IF.B.4 F.IF.C.7.A

Calculate and compare the average rate of change for linear, exponential, and quadratic functions.

F.IF.B.4 F.IF.B.6 F.LE.A.3

Topic B: Factoring and Solutions of Quadratic Equations

Factor quadratic expressions using the greatest common factor. Demonstrate equivalence between expressions by multiplying polynomials.

A.APR.A.1 A.SSE.A.2 A.SSE.B.3.A

Identify solutions to quadratic equations using the zero product property (equations written in intercept form).

A.APR.B.3 F.IF.C.8.A

Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).

A.SSE.A.1.A A.SSE.B.3.A

Factor quadratic equations and identify solutions (when leading coefficient does not equal 1).

A.SSE.A.1.A A.SSE.B.3.A

Factor special cases of quadratic equations—difference of two squares.

A.SSE.A.1.A A.SSE.A.2 A.SSE.B.3.A

Factor special cases of quadratic equations—perfect square trinomials.

A.SSE.A.2 A.SSE.B.3.A

Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).

A.SSE.B.3.A F.IF.C.8.A F.IF.C.9

Solve quadratic equations by taking square roots.

A.REI.B.4.B

Graph quadratic functions using $${x-}$$intercepts and vertex.

A.APR.B.3 F.IF.B.4 F.IF.C.7.A F.IF.C.8.A

Topic C: Interpreting Solutions of Quadratic Functions in Context

Interpret quadratic solutions in context.

A.CED.A.1 F.IF.B.4 F.IF.B.5 F.IF.C.8.A

Quadratic Functions and Solutions

Objective

Common Core Standards

Core Standards

Interpreting Functions

Interpreting Functions

Criteria for Success

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Additional Practice

Lesson Map

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