Unit 1 Polynomial Functions Check your understanding From

Unit 1: Polynomial Functions

Check your understanding …. From the graph given, determine the equation of the function.

1. 5: Finite Differences Today we are going to investigate the information we can get from the table of values of a function. We will be using finite differences to determine the degree of the function as well as the value of the leading coefficient.

Linear Functions In grade 9, we learned that the first differences of linear relations are constant – i. e. lines have a constant rate of change. The first difference is also the slope of the line.

Quadratic Functions In grade 10, we learned that the 2 nd differences of quadratic functions were constant and used this to differentiate between linear and quadratic functions. Can you see a connection between the 2 nd difference and the leading coefficient?

Cubic Functions Can you see a connection between the 3 rd difference and the leading coefficient?

Quartic Functions Can you see a connection between the 4 th difference and the leading coefficient?

Leading Coefficient & Finite Differences

Leading Coefficient & Finite Differences

Leading Coefficient & Finite Differences

Example: (a) Complete the finite difference table.

Example: (b) Determine the type of polynomial function modeled by the data. (c) Determine the value of the leading coefficient.

Challenge Determine the equation of the polynomial function that models the data found in the following table.

Summary

Practice Work P. 8 -9 #1, 6