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NSW Y11 Maths Standard NSW Y11 Maths Advanced NSW Y11 Maths Extension 1

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Functions Polynomials Inverse Trig Functions and Identities Rates of Change Permutations and Combinations

NSW Y11 Maths - Extension 1 Polynomials Polynomial Graphs

Resources for Polynomial Graphs

  • Questions

    18

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  • Video Tutorials

    2


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  • HSC Questions

    4

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Polynomial Graphs Theory

NSW Syllabus Reference

NSW Syllabus Reference: ME-F2.2: Sums and products of roots of polynomials. This will require student to 

  • solve problems using the relationships between the roots and coefficients of quadratic, cubic and quartic equations
  • determine the multiplicity of a root of a polynomial equation
  • graph a variety of polynomials and investigate the link between the root of a polynomial equation and the zero on the graph of the related polynomial function

Ref: https://educationstandards.nsw.edu.au/

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Videos

Videos relating to Polynomial Graphs.

  • Polynomial Graphs - Video- Polynomial Graphs

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  • Polynomial Graphs - Video - Graphing Polynomial Functions Using End Behavior, Zeros, and Multiplicities

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Theory

For a polynomial of odd degree always has at least one real zero. The graph must cut the \(x\)-axis at least once.

At least one maximum or minimum value of \(y = P(x)\) occurs between any two distinct zeros.

For a polynomial of odd degree, the ends of the graph go in opposite directions.

For a polynomial of even degree, the ends of the graph go in the same direction.

When the graph of \(y = P(x)\) meets the \(x\)-axis, it may cut (single zero), touch (double zero) or cut it at a point of inflexion (triple zero).