Graphing Cubic Equations
The applet below has 4 different cubic functions, including their roots. You can cycle through the functions, as well as change some values of the functions. Play around with the app, and then answer the questions below in your notebook.
Question 1: Consider the function f_1(x), which has three real, distinct zeros: b, c, and d, and a leading coefficient a. How does "a" affect the graph?
What is the geometrical significance of b, c, and d?
Draw some examples, illustrating the above answers.
Question 2: Consider the function f_2(x), which has two real zeroes, with one repeated, and a leading coefficient a. What is the geometrical significance of the squared factor?
Draw an example, illustrating the above answers.
Question 3: Consider the function f_3(x), which has one zero, repeated three times, and a leading coefficient a. What is the geometrical significance of the cubed factor?
Draw an example, illustrating the above answer.
Question 4: Consider the function f_4(x), which has one real zero, and two complex zeros (so an irreducible quadratic, with a negative discriminant). Compare this function to the previous function, f_3(x).
Draw an example, illustrating the above answer.