HSC Together Year 11 Maths Advanced: Identifying the Shape and Features of a Polynomial Function

• Working With Functions
• Trigonometric Functions
• Calculus
• Exponential and Logarithmic Functions
• Statistical Analysis
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Identifying the Shape and Features of a Polynomial Function

How do I identify the shape and features of a polynomial function?

In this post, we are identifying the shape and features of the graphs of a polynomial function] of any degree in factored form and sketch their graphs, as a part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Further Functions and Relations.

The shape of a polynomial function will depend on two things, the degree and sign of the leading coefficient. If the:

• Degree is an even number and the leading coefficient is positive, the ends of the polynomial will end in the first and second quadrant
• Degree is an even number and the leading coefficient is negative, the ends of the polynomial will end in the third and fourth quadrant
• Degree is an odd number and the leading coefficient is positive, the ends of the polynomial will end in the first and third quadrant
• Degree is an odd number and the leading coefficient is negative, the ends of the polynomial will end in the second and fourth quadrant

How do I determine the polynomial end behaviour?

The following two videos cover how you can determine the polynomial end behaviour using properties of a polynomial.

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