Texas Instruments TI-83 Guide

Using a TI-83/TI-84 Graphing Utility:
I. Find and store the roots/zeros of
2
( ) 12 3
f x x x
= − +
.
Graph Y
1
=
2
12 3
x x
− +
.
Zoom 6 for the standard window… [-10, 10]
1
x [-10, 10]
1
.
Zoom Out (Zoom 3 ENTER) to view the other root.
Find the left root:
Press 2
nd
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
nd
MODE (to QUIT GRAPH screen and view HOME screen).
Press X,T, θ ,n STO  ALPHA A ENTER.
Find the right root:
Press 2
nd
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
nd
MODE (to QUIT GRAPH screen and view HOME screen).
Press X,T, θ ,n STO  ALPHA B ENTER.
2
( ) 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
2
( ) 3 2
g x x
= −
.
Graph Y
1
=
cos( )
x
and Y
2
=
2
3 2
x
−
. Are you in radian mode?
Zoom 6 for the standard window… [-10, 10]
1
x [-10, 10]
1
.
Change the window to view the intersection points….[-3, 3]
1
x [-5, 5]
1
.
Press GRAPH.
Find the left intersection point:
Press 2
nd
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
nd
MODE (to QUIT GRAPH screen and view HOME screen).
Press X,T, θ ,n STO  ALPHA A ENTER.
Store left y-coordinate as C:
Press 2
nd
MODE (to QUIT GRAPH screen and view HOME screen).
Press ALPHA Y STO  ALPHA C ENTER.

Find the right intersection point:
Press 2
nd
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
nd
MODE (to QUIT GRAPH screen and view HOME screen).
Press X,T, θ ,n STO  ALPHA B ENTER.
Store left y-coordinate as D:
Press 2
nd
MODE (to QUIT GRAPH screen and view HOME screen).
Press ALPHA Y STO  ALPHA D ENTER.
( ) cos( )
f x x
=
and
2
( ) 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
1
=
3 2
5 3
x x x
− − −
.
Zoom 6 for the standard window… [-10, 10]
1
x [-10, 10]
1
.
Find the maximum value of
3 2
( ) 5 3
f x x x x
= − − −
:
Press 2
nd
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
1
x
= −
.
See the table of values!
Find the minimum value of
3 2
( ) 5 3
f x x x x
= − − −
:
Press 2
nd
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
x
≈
.