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Notes
Step & Key Operation
*Use either pen touch or cursor to operate.
Display
EL-9650/9600c Graphing Calculator
2-1
2
-
2
View both graphs.
3
-
2
View both graphs.
Notice that the multiplication of
2 pinches or closes the basic
y=x
2
graph. This demonstrates
the fact that multiplying an a
(> 1) in the standard form
y = a
(x - h)
2
+ k
will pinch or close
the basic graph.
4
-
1
Change the equation in Y2 to
y = -2x
2
.
Notice that the multiplication of
-2 pinches or closes the basic
y =
x
2
graph and flips it (reflects
it) across the x-axis. This dem-
onstrates the fact that multiply-
ing an a (<-1) in the standard form y = a (x - h)
2
+ k
will pinch or close the basic graph and flip it (reflect
it) across the x-axis.
*
Change the equation in Y2 to y = x
2
+2.
2
-
1
*
3
-
1
Change the equation in Y2 to y = 2x
2
.
*
The EL-9650/9600c/9450/9400 allows various quadratic equations to be graphed
easily. Also the characteristics of quadratic equations can be visually shown
through the relationship between the changes of coefficient values and their
graphs, using the Substitution feature.
4
-
2
View both graphs.
2nd F
GRAPH
Y=
SUB
2
0
ENTER ENTER
GRAPH
Y=
2nd F
SUB
2
0
ENTER
ENTER
GRAPH
Y=
2nd F
SUB
(
-
)
2
ENTER
Notice that the addition of 2 moves
the basic y =x
2
graph up two units
and the addition of -2 moves the
basic graph down two units on
the
y-axis.
This demonstrates the
fact that adding k (>0) within the standard form y = a (x -
h)
2
+ K will move the basic graph up K units and placing k
(<0) will move the basic graph down K units on the y axis.
Using this Handbook
This handbook was produced for practical application of the SHARP EL-9650/9600c and
EL-9450/9400 Graphing Calculator based on exercise examples received from teachers
actively engaged in teaching. It can be used with minimal preparation in a variety of
situations such as classroom presentations, and also as a self-study reference book.
We would like to express our deepest gratitude to all the teachers whose cooperation we received in editing this
book. We aim to produce a handbook which is more replete and useful to everyone, so any comments or ideas
on exercises will be welcomed.
(Use the attached blank sheet to create and contribute your own mathematical problems.)
Thanks to Dr. David P. Lawrence at Southwestern Oklahoma State University for the use of his
teaching resource book (Applying Pre-Algebra/Algebra using the SHARP EL-9650/9600c Graphing
Calculator).
Other books available:
Graphing Calculator EL-9450/9400 TEACHERS’ GUIDE
•
When you see the sign
*
on the key:
*
means same series of key strokes can be done with screen touch on the EL-9650/9600c.
(
*
: for the corresponding key;
*
: for the corresponding keys underlined.)
Key operations may also be carried out with the cursor (not shown).
•
Different key appearance for the EL-9450/9400: for example
➔
X/ /T/
n
X
/
T
EL-9650/9600c Graphing Calculator
Slope and Intercept of Quadratic Equations
A quadratic equation of y in terms of x can be expressed by the standard form y = a (x -h)
2
+
k, where a is the coefficient of the second degree term ( y = ax
2
+ bx + c) and ( h, k) is the
vertex of the parabola formed by the quadratic equation. An equation where the largest
exponent on the independent variable x is 2 is considered a quadratic equation. In graphing
quadratic equations on the calculator, let the x- variable be represented by the horizontal
axis and let y be represented by the vertical axis. The graph can be adjusted by varying the
coefficients a, h, and k.
2-1
There may be differences in the results of calculations and graph plotting depending on the setting.
Return all settings to the default value and delete all data.
As the Substitution feature is only available on the EL-9650/9600c, this section does not apply to the EL-9450/9400.
Before
Starting
Graph various quadratic equations and check the relation between the graphs and
the values of coefficients of the equations.
Example
1.
Graph y = x
2
and y = (x-2)
2
.
2.
Graph y = x
2
and y = x
2
+2.
3.
Graph y = x
2
and y = 2x
2
.
4.
Graph y = x
2
and y = -2x
2
.
1
-
1
Enter the equation y = x
2
for Y1.
Notes
Step & Key Operation
*Use either pen touch or cursor to operate.
Display
1
-
2
Enter the equation y = (x-2)
2
for Y2
using Sub feature.
*
*
*
( )
Notice that the addition of -2
within the quadratic operation
moves the basic y =x
2
graph
right two units (adding 2 moves
it left two units) on the x-axis.
This shows that placing an h (>0) within the standard
form y = a (x - h)
2
+ k will move the basic graph right
h units and placing an h (<0) will move it left h units
on the x-axis.
View both graphs.
1
-
3
X
/
θ
/
T
/
n
ENTER
Y=
x
2
EZ
1
1
2
1
0
ENTER ENTER
ENTER
ENTER
GRAPH
ENTER
ALPHA
C
2nd F
SUB
Merits of Using the EL-9650/9600c/9450/9400
Highlights the main functions of the calculator relevant
to the section
Introduction
Explanation of the section
Example
Example of a problem to be
solved in the section
Before Starting
Important notes to read
before operating the calculator
Step & Key Operation
A clear step-by-step guide
to solving the problems
Display
Illustrations of the calculator
screen for each step
Notes
Explains the process of each
step in the key operations