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Graphing Reciprocals of Quadratics: Find the Asymptotes

NL.SO.2200AN2

Conversion between entire radicals and mixed radicals

auto-gen

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Dividing radicals

Rationalize the denominator

NL.SO.2200AN3

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

NL.SO.2200AN4

Partial fraction decomposition

Simplifying rational expressions and restrictions

NL.SO.2200AN5

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

NL.SO.2200AN6

Solving rational equations

Applications of rational equations

NL.SO.2200RF1

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

NL.SO.2200RF10

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

NL.SO.2200RF11

Graphing reciprocals of linear functions

Sigma notation

Graphing reciprocals of quadratic functions

NL.SO.2200RF2

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

NL.SO.2200RF3

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

NL.SO.2200RF4

Applications of quadratic functions

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Completing the square

Completing the Square

NL.SO.2200RF5

Solving polynomial equations by iteration

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

NL.SO.2200RF6

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

NL.SO.2200RF7

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

NL.SO.2200RF8

Solving quadratic inequalities

NL.SO.2200RF9

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Graphing systems of linear inequalities

Applications of inequalities

NL.SO.2200T1

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

NL.SO.2200T2

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NL.SO.2200T3

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Parent Assignments

Challenge Zone

Foundation Review

Advanced Mathematics 2200

Algebra and Number

Relations and Functions

math

Ex.1

Graphing the reciprocal of a quadratic using the five-step method

Ex.2

Reciprocal of a quadratic with no x-intercepts

Ex.3

Graphing the reciprocal of a quadratic with two x-intercepts

Ex.4

Reciprocal of a quadratic with no x-intercepts or invariant points

This lesson shows how to graph the reciprocal of a quadratic function by finding the zeros of the quadratic, which become vertical asymptotes, mapping its vertex to a maximum or minimum point, and reading sign changes across the three possible cases: two real roots, one repeated root, or no real roots at all.

Graphing Reciprocals of Quadratic Functions | StudyPug

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Overview

How to Graph the Reciprocal of a Quadratic Function

What You'll Learn

Identify the zeros of the quadratic denominator to locate every vertical asymptote on the graph.

Map the vertex of the quadratic to the corresponding maximum or minimum point on the reciprocal graph.

Analyze the sign of the quadratic in each interval to decide whether a branch lies above or below the x-axis.

Recognize the horizontal asymptote at y = 0 that every reciprocal quadratic graph shares.

Compare the two-root, repeated-root, and no-root cases to predict the overall shape before plotting.

Sketch smooth curved branches that hug each asymptote without ever touching or crossing it.

What You'll Practice

Plotting asymptotes and invariant points from quadratic functions

Finding reciprocal values of vertices, intercepts, and selected points

Graphing reciprocals of upward and downward-opening parabolas

Connecting points while tracing along horizontal and vertical asymptotes

Why This Matters

This Unit Includes

4 Video lessons

Practice exercises

Learning resources

Skills

Reciprocal Functions

Quadratic Functions

Asymptotes

Invariant Points

Function Transformations

Graphing

Vertices