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.
Part 1
