Polynomials

1. Sketch the graph of y=(x-2)(x-1)(x+1) and consider the following:
   • What happens to their graph for large negative and large positive x values?
   • What are the domain and range?
   • What would happen to their graph if you changed it to y=(x-2)(x-1)(x+2) or y=-(x-2)(x-1)(x+1)?
   • What do you think would happen if there were only two x-intercepts or only one x-intercept?
2. Consider the following:
   • How many times do you suspect the graph of y=(x-0)(x-1)(x-2) will cross the x-axis?
   • At what points do you think the graph of y=(x-0)(x-1)(x-2) will cross the x-axis?
   • How many local extrema do you expect to see in the graph of y=(x-0)(x-1)(x-2)?
   • What do you expect the domain and range of the function y=(x-0)(x-1)(x-2) to be?
   • How do you think the graph of y=(x-0)(x-1)(x-2) will be different than the graph of y= -(x-0)(x-1)(x-2)?

3. Consider the following:
   • What is the domain and range of a function of the form y=a(x-s)(x-t)(x-u)?
   • What is the end behaviour of a cubic function if the leading coefficient is positive? negative?
   • How many local extrema does a cubic function have? What if the function had one or more zeros the same? Would this change your answer?

More about Polynomials.

See the matching Ontario Mathematics Curriculum expectations.