Texas-instruments PLUS TI-89 User Manual download pdf (Page 419)

100

101

402 Chapter 23: Activities

23ACTS.DOC TI-89/TI-92 Plus: Activities (English) Susan Gullord Revised: 02/23/01 1:24 PM Printed: 02/23/01 2:20 PM Page 402 of 26

Perform the following steps to expand the cubic polynomial

1)(x

)(x+

)

, find the absolute value of the function, graph the

modulus surface, and use the

Trace

tool to explore the modulus

surface.

1. On the Home screen, use the

expand()

function to expand

the cubic expression

1)(x

) (x+

)

and see the first

polynomial.

2. Copy and paste the last answer

to the entry line and store it in

the function

f(x)

3. Use the

abs()

function to find

the absolute value of

f(x+y

)

(This calculation may take

about 2 minutes.)

4. Copy and paste the last answer

to the entry line and store it in

the function

z1(x,y)

5. Set the unit to 3D graph mode,

turn on the axes for graph

format, and set the Window

variables to:

eye= [20,70,0]

x= [

2,2,20]

y= [

2,2,20]

z= [

1,2]

ncontour= [5]

Visualizing Complex Zeros of a Cubic Polynomial

This activity describes graphing the complex zeros of a cubic

polynomial. Detailed information about the steps used in this

example can be found in Chapter 3: Symbolic Manipulation

and Chapter 10: 3D Graphing.

Visualizing Complex

Roots

Hint: Move the cursor into

the history area to highlight

the last answer and press

, to copy it to the entry

line.

Note: The absolute value of

a function forces any roots

to visually just touch rather

than cross the x axis.

Likewise, the absolute value

of a function of two variable

will force any roots to

visually just touch the xy

plane.

Note: The graph of

z1(x,y)

will be the modulus surface.

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Texas-instruments PLUS TI-89 User Manual Page 419

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