Texas Instruments TI-83 Guide

Using a TI-83/TI-84 Graphing Utility:

I. Find and store the roots/zeros of

( ) 12 3

f x x x

= − +

Graph Y

12 3

x x

− +

Zoom 6 for the standard window… [-10, 10]

x [-10, 10]

Zoom Out (Zoom 3 ENTER) to view the other root.

Find the left root:

Press 2

TRACE 2: zero.

Left Bound? Press ENTER on

0 3

x y

= =

Right Bound? Move cursor to the right to get a negative y-coordinate.

Press ENTER on

.85106383 6.488456

x y

= = −

Guess? Press ENTER.

Store left root as A:

Press 2

MODE (to QUIT GRAPH screen and view HOME screen).

Press X,T,

,n STO



ALPHA A ENTER.

Find the right root:

Press 2

TRACE 2: zero.

Left Bound? Move cursor to the right to get a negative y-coordinate.

Press ENTER on

11.06383 7.357628

x y

= = −

Right Bound? Move cursor to the right to get a positive y-coordinate.

Press ENTER on

11.914894 1.9859665

x y

= =

Guess? Press ENTER.

Store right root as B:

Press 2

MODE (to QUIT GRAPH screen and view HOME screen).

Press X,T,

,n STO



ALPHA B ENTER.

( ) 12 3

f x x x

= − +

has roots/zeros at approximately

(0.225,0)

and

(11.745,0)

Calculate A – B.

A – B

≈

-11.48912529 or A – B

≈

-11.489

NOTE: If you used the rounded values to compute the new problem, you would get

A – B

≈

-11.49…. which is incorrect!

Find and store the intersections of

( ) cos( )

f x x

and

( ) 3 2

g x x

= −

Graph Y

cos( )

and Y

3 2

−

Are you in radian mode?

Zoom 6 for the standard window… [-10, 10]

x [-10, 10]

Change the window to view the intersection points….[-3, 3]

x [-5, 5]

Press GRAPH.

Find the left intersection point:

Press 2

TRACE 5: intersect.

First Curve? Move cursor left closer to the left point of intersection.

Press ENTER .

Second Curve? Press ENTER.

Guess? Press ENTER.

Store left x-coordinate as A:

Press 2

MODE (to QUIT GRAPH screen and view HOME screen).

Press X,T,

,n STO



ALPHA A ENTER.

Store left y-coordinate as C:

Press 2

MODE (to QUIT GRAPH screen and view HOME screen).

Press ALPHA Y STO



ALPHA C ENTER.

Find the right intersection point:

Press 2

TRACE 5: intersect.

First Curve? Move cursor right closer to the right point of intersection.

Press ENTER .

Second Curve? Press ENTER.

Guess? Press ENTER.

Store right x-coordinate as B:

Press 2

MODE (to QUIT GRAPH screen and view HOME screen).

Press X,T,

,n STO



ALPHA B ENTER.

Store left y-coordinate as D:

Press 2

MODE (to QUIT GRAPH screen and view HOME screen).

Press ALPHA Y STO



ALPHA D ENTER.

( ) cos( )

f x x

and

( ) 3 2

g x x

= −

have points of intersection at approximately

(

)

0.930,0.597

−

and

(

)

0.930,0.597

Calculate A – B.

A – B

≈

-1.860981941 or A – B

≈

-1.861

NOTE: If you used the rounded values to compute the new problem, you would get

A – B

≈

-1.86…. which is incorrect!

Calculate C + D.

C + D

≈

1.194880677 or C + D

≈

1.195

NOTE: If you used the rounded values to compute the new problem, you would get

C + D

≈

1.194…. which is incorrect!

Find maximum and minimum values of

3 2

( ) 5 3

f x x x x

= − − −

Graph Y

3 2

5 3

x x x

− − −

Zoom 6 for the standard window… [-10, 10]

x [-10, 10]

Find the maximum value of

3 2

( ) 5 3

f x x x x

= − − −

Press 2

TRACE 4: maximum.

Left Bound? Move cursor to the left to get a y-coordinate that is less than

the relative max.

Press ENTER on

1.489362 1.075089

x y

= − = −

Right Bound? Move cursor to the right to get a y-coordinate that is less than the max.

Press ENTER on

0.4255319 1.130472

x y

= − = −

Guess? Press ENTER.

3 2

( ) 5 3

f x x x x

= − − −

has a relative maximum value of 0 at

= −

See the table of values!

Find the minimum value of

3 2

( ) 5 3

f x x x x

= − − −

Press 2

TRACE 3: minimum.

Left Bound? Move cursor to the right to get a y-coordinate that is more than

the relative min.

Press ENTER on

0.63829787 6.338856

x y

= = −

Right Bound? Move cursor to the right to get a y-coordinate that is less than the max

Press ENTER on

2.3404255 7.359824

x y

= = −

Guess? Press ENTER.

3 2

( ) 5 3

f x x x x

= − − −

has a relative minimum value of -9.481 at

1.667

≈

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