Cubic Investigation

Investigation Task.

Note the Sliders on the top left. These can change the value of a b c and d in the formulas to the right. Selected the factorised Cubic form (Blue) and move the sliders to see the effect on the Graph.

The "a" Value.

What is the effect on the graph of changing the "a" Value? Explain what happens when "a" is positive, negative and also when "a" is Zero.

More on "a"

Select the form. This is also known as the general form. (The graph should now be red). The graph itself may be different to what you had before. Ignoring this does adjusting the value of "a" have the same effect here as in the factorised form?

Select all that apply

A
Yes
B
No

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Factors

Go back to the factorised form. Set the "a" value at 1, then move the other sliders. Some major changes occur to the graph as each of these is changed. Focusing particularly on the roots, what is the effect of changing the b,c and d values?

Create the Following Graph.

By moving the sliders in the Factorised form create a graph with a=1 and roots at -2 ,1 and 2. The software shows double negatives but the formula is essentially . Expand this form out into the general form. What is the general form?

Select all that apply

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Text Book Work

Return the to Text book and read through Exercise 9L the cubics here are all in the form

(this means that b and c are equal to zero in the general form. (The red graph). You can continue to use the geogebra graphing tool to help you understand the questions in the textbook. Read through the examples and do the questions.