Sharp EL-9400, EL-9600c, EL-9650 manual Graphing Hyperbolas

Page 54

EL-9650/9600c/9450/9400 Graphing Calculator

Graphing Hyperbolas

The standard equation for a hyperbola can take one of two forms:

( x - h )2

-

( y - k )2

= 1

with vertices at ( h ± a, k ) or

a2

b 2

 

 

 

( x - k )2

-

( y - h)2

 

= 1

with vertices at ( h, k ± b ).

a2

b 2

 

 

 

There is a problem entering this equation in the calculator graphing list for two reasons:

a)it is not a function, and only functions can be entered in the Y= list locations.

b)the functions entered in the Y= list locations must be in terms of x, not y.

To draw a graph of a hyperbola, consider the “top” and “bottom” halves of the hyperbola as two different parts of the graph because each individual is a function. Solve the equation of the hyperbola for y and enter the two parts in two locations of the Y= list.

Example

Graph a hyperbola in rectangular mode. Solve the equation for y to put it in the standard form.

Graph the hyperbola x 2 + 2x - y 2 - 6y + 3 = 0

Before There may be differences in the results of calculations and graph plotting depending on the setting. Starting Return all settings to the default value and delete all data.

Set the zoom to the decimal window:

ZOOM A * (

ENTER ALPHA

)

*

7*

Step & Key Operation

Display

Notes

(When using EL-9650/9600c)

(When using EL-9650/9600c)

 

*Use either pen touch or cursor to operate.

 

 

1

2

Solve the equation for y completing the square.

Enter

Y1 = √ x 2 + 2x + 12

Y2 = Y1 -3

Y3 = -Y1 -3

Y=

 

2nd F

 

√

 

X/ /T/n

 

x2

 

 

 

+

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

X/θ /T/n

 

+

1

 

2

 

ENTER

*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VARS

 

A

*

ENTER

 

 

1 *

 

—

 

3

 

ENTER

*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

( )

 

VARS

 

 

 

 

ENTER

1

 

 

 

 

—

 

3

 

-

 

 

A

*

 

 

*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Turn off Y1 so that it will not graph.

* ENTER *

x 2 + 2x - y 2 -6y= -3

x 2 + 2x - (y 2 + 6y + 9) = -3 -9 x 2 + 2x - (y +3)2 = -12

(y + 3)2 = x 2 + 2x + 12

y+ 3 = +√ x 2 + 2x + 12 y = +√ x 2 + 2x + 12 - 3

10-4

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Page 53 Page 55
Contents EL-9650/9600c/9450/9400 Contents Read this first Always read Before StartingUsing this Handbook IntroductionSlope and Intercept of Linear Equations Enter the equation y = x for Y2 Parallel and Perpendicular Lines 2View the graphs Slope and Intercept of Quadratic Equations 1Change the equation in Y2 to y = x 2+2 Shifting a Graph of Quadratic Equations 1Move the graph y = x 2 to the right by 1Access the Solver feature This screen will appear a few 4Enter the values L=15,000, I=0.09, N=48 Access the Solver feature 10π 200 15π1Access the Solver feature 5Solve for the height and enter a starting point Graphing Polynomials and Tracing to Find the Roots 1Move the tracer near the left-hand root Graphing Polynomials and Jumping to Find the Roots EL-9650/9600c/9450/9400 Graphing Calculator Solving a System of Equations by Graphing or Tool Feature 1Access the Tool menu. Select the number of variables Entering and Multiplying Matrices Enter a 3 x 3 matrix B Solving a System of Linear Equations Using Matrices 17 0.83 = 0.5 0.5 17 0.17 Solving Inequalities 1Enter y = 34 2x for Y1 and y = 5 x for Y2 Solving Double Inequalities 2x 5 ≥= 2x 5 and y = 7 intersect at 6,7 System of Two-Variable Inequalities + y ≤Graphing Solution Region of Inequalities + y ≥Continuing key operations omitted Slope and Intercept of Absolute Value Functions If x ≥3View the graph Shifting a graph of Absolute Value Functions = x y = Solving Absolute Value Equations Solve an absolute value equation 5 4x =Solving Absolute Value Inequalities 2Set up shading = -4, y =Evaluating Absolute Value Functions Evaluate Graphing Rational Functions + 1x Solving Rational Function Inequalities Graphing Parabolas = y 2 + 2 = y = +- √ x +1Change to parametric mode Graphing Circles Graph x 2 2x + y 2 + 4y =3Turn off Y1 so that it will not graph Graphing Ellipses View the graph in the new window Graphing Hyperbolas Zoom out the screen Key pad for the Sharp EL-9650/9600c Calculator Key pad for the Sharp EL-9450/9400 Calculator We thank you for your cooperation in this project Step Sharp Corporation OSAKA, Japan
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EL-9650, EL-9600c, EL-9400 specifications

The Sharp EL-9400 and EL-9450 are advanced programmable scientific calculators designed for professionals and students alike. Renowned for their versatile functionality and user-friendly interface, these calculators are popular in the fields of engineering, mathematics, and the sciences.

One of the hallmark features of the EL-9400 and EL-9450 is their extensive range of built-in functions. These calculators allow users to perform a variety of mathematical operations, including basic arithmetic, statistical calculations, complex number operations, and calculus functions. They support both decimal and fraction calculations, making them suitable for diverse mathematical applications.

Both models come equipped with a large, easy-to-read display, enhancing user experience by allowing for clear visibility of numbers, symbols, and results. The display is particularly beneficial when working with extensive calculations or graphical representations, as it helps users track their inputs and outputs with ease.

The programmability of the EL-9400 and EL-9450 sets them apart from standard calculators. Users can create custom programs to automate repetitive calculations, save time, and increase efficiency during work or study sessions. This programmable capability is particularly advantageous for students tackling complex mathematical problems or professionals managing extensive data sets.

With their advanced graphing capabilities, these calculators allow users to plot functions and analyze their behavior over a defined range. The graphing feature is user-friendly, offering options to zoom in and out, providing a better understanding of mathematical concepts and aiding in visualization.

Another notable characteristic of the EL-9400 and EL-9450 is their robust memory function. These calculators can store multiple equations and values, enabling users to retrieve and re-use data without the need to re-enter it. This function is essential for tasks requiring multiple steps and intermediate values.

In terms of durability, the Sharp EL series is designed to withstand the rigors of academic and professional environments. These calculators are built with high-quality materials, ensuring longevity and reliability during extensive use.

Overall, the Sharp EL-9400 and EL-9450 stand out as powerful tools for anyone needing a reliable computing resource. Their combination of programmable features, comprehensive function sets, and user-friendly design makes them invaluable assets for students and professionals engaged in advanced mathematics and scientific calculations. With these calculators, users are equipped to tackle challenges and explore complex mathematical concepts with confidence.
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