Classroom Resource

Zeroes and Intercepts of Polynomials: Function Intercepts Interactive

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This interactive will help students practice identifying zeroes and intercepts of polynomial functions using graphical representations. 

In this interactive, students will:

    • move the red line to see the intersections between the blue function and the red line.
      (The blue points are the places where the red line intersects the blue function.)
    • hover over the blue intercepts to see their coordinate values.
Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.6

Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

Unpacked Content

UP:MA19.PRE.6

Vocabulary

  • Zeros
  • Fundamental Theorem of Algebra
  • Quadratic Polynomial

Knowledge

Students know:
  • The definition of the degree of a polynomial.
  • The difference between real and complex roots.

Skills

Students are able to:
  • Find roots of a polynomial algebraically and/or graphically.
  • Rewrite an imaginary number as a complex number.

Understanding

Students understand that:
  • The degree of a polynomial determines the number of roots, some which may be real, complex, or used more than once.
  • Only real roots will be x-intercepts on a graph.
Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.26

Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph.

Unpacked Content

UP:MA19.PRE.26

Vocabulary

  • Rational functions
  • Horizontal asymptote
  • Vertical asymptote
  • Slant asymptote
  • Amplitude
  • Period
  • Phase shift
  • Domain
  • Range
  • Frequency
  • Midline

Knowledge

Students know:
  • Techniques for graphing,
  • Key features of graphs of functions.

Skills

Students are able to:
  • Determine horizontal, vertical, and slant asymptotes of rational functions, and use these to sketch the graphs, identifydomains and ranges, and end behaviors.
  • Sketch the graphs, analyze, compare, and identify domains and ranges of the basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
  • Find the amplitude and period of a trigonometric function and use these characteristics to sketch its graph.
  • Identify and sketch translations of trigonometric graphs (vertical shifts and phase shifts).
  • Evaluate, graph and identify the domains and ranges of inverse trigonometric functions.

Understanding

Students understand that:
  • A rational function is the ratio of two polynomial functions.
  • Rational functions contain restrictions on their domains and/or ranges. Therefore, their graphs contain asymptotes, holes, and/or discontinuity.
  • The graphs of rational functions vary, yielding various patterns.
  • Using algebraic methods to manipulate and/or solve the equation of a rational function can help determine important properties such as its zeroes, intercepts, asymptotes, domain, range, types of discontinuity, and end behavior.
  • Key characteristics (rational and trigonometric) of functions can help you visualize the sketch of it's graph and can lead to more effective and efficient graphing methods.
Link to Resource
https://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=MAT.ALG.606&q…

Resource Provider

Other

Resource Provider other

CK-12
Accessibility
License

License Type

CUSTOM

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Comments or Notes

Students must create a free account to access the interactive.

Approved Date

habradley
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