Polynomial Functions in Context

Degree from a graph or a table of differences, end behaviour, intercepts, and polynomial regression models.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

What is the degree of y = 3x² − 2x⁴ + x − 7?
The graph of a polynomial function is shown. Which describes its degree and leading coefficient?
The table shows values of a polynomial function at equally spaced x. Using finite differences, what is the degree of the function?
What is the end behaviour of y = x⁴ − 3x² + 1?
The graph of a cubic function is shown. What is its y-intercept?
How many distinct real zeros does the function graphed have?
A cubic regression of a business's monthly profit P, in thousands of dollars, against month t gives P = 0.2t³ − 3t² + 12t + 5. What does the 5 represent?
For the profit model P = 0.2t³ − 3t² + 12t + 5, with P in thousands of dollars, what is P when t = 6? Give the answer correct to the nearest tenth.
Squares of side x cm are cut from the corners of a 20 cm by 12 cm sheet, and the sides are folded up to make an open box with volume V = x(20 − 2x)(12 − 2x). What is the volume, in cubic centimetres, when x = 2?
For the box V = x(20 − 2x)(12 − 2x), which domain makes sense in the context?