NSW Y11 Maths - Extension 1 Polynomials Polynomial Graphs

Polynomial Graphs Videos How to buy Theory

Resources for Polynomial Graphs

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

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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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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).