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Sharp EL-9650 manual

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Table of contents for the manual

  • Page 1

    Graphing Calculator EL-9650/9600c/9450/9400 Handbook V ol. 1 Algebra EL-9650 EL-9450[...]

  • Page 2

    1. Linear Equations 1-1 Slope and Intercept of Linear Equations 1-2 Parallel and Perpendicular Lines 2. Quadratic Equations 2-1 Slope and Intercept of Quadratic Equations 2-2 Shifting a Graph of Quadratic Equations 3. Literal Equations 3-1 Solving a Literal Equation Using the Equation Method (Amortization) 3-2 Solving a Literal Equation Using the G[...]

  • Page 3

    1. Always read “Befor e Starting” The key operations of the set up condition are written in “Before Starting” in each section. It is essential to follow the instructions in order to display the screens as they appear in the handbook. 2. Set Up Condition As key operations for this handbook are conducted from the initial condition, reset all [...]

  • Page 4

    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 [...]

  • Page 5

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) S lope and Inter cept of Linear E quations A linear equation of y in ter ms of x can be expressed by the slope-intercept form y = mx+b , where m is the slope and b is th[...]

  • Page 6

    Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) EL-9650/9600c/9450/9400 Graphing Calculator Notes Enter the equation y = - x for Y2. View both graphs. Notice how Y2 decreases (going down from left to right) instead of increasing (going up from left to right). Negativ[...]

  • Page 7

    EL-9650/9600c/9450/9400 Graphing Calculator P arallel and P erpendicular Lines 1-2 1. Graph the equations y = 3 x + 1 and y = 3 x + 2. 2. Graph the equations y = 3 x - 1 and y = - x + 1 . Enter the equations y = 3 x + 1 for Y1 and y = 3 x + 2 for Y2. View the graphs. 1 - 1 Graph parallel lines and perpendicular lines. 1 - 2 Example Enter the equati[...]

  • Page 8

    Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) EL-9650/9600c/9450/9400 Graphing Calculator Notes 1-2 View the graphs. These lines have slopes that are negative reciprocals of each other ( m = - ). They are called perpendicular. Note that these intersecting lines for[...]

  • Page 9

    EL-9650/9600c Graphing Calculator S lope and I nter cept 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 wher[...]

  • Page 10

    Step & Key Operation *Use either pen touch or cursor to operate. Display EL-9650/9600c Graphing Calculator Notes 2-1 2 - 2 View both graphs. 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[...]

  • Page 11

    EL-9650/9600c/9450/9400 Graphing Calculator 2-2 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. Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) S [...]

  • Page 12

    Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) EL-9650/9600c/9450/9400 Graphing Calculator Notes 2-2 Move the graph y = x 2 to the right b y 3. 2 - 1 (three times) * 3 - 3 Save the new graph and observe the changes in the graph and the equation. Notice that pinching[...]

  • Page 13

    EL-9650/9600c Graphing Calculator 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. Notes Step & Key Operation *Use either pen touch or cursor to operate. Display 3-1 S olving a Literal Equation U sing the Equation M ethod (Amortizat[...]

  • Page 14

    Step & Key Operation *Use either pen touch or cursor to operate. Display EL-9650/9600c Graphing Calculator Notes 3-1 Save this formula. 2 - 1 Give the formula the name AMORT. 2 - 2 The monthly payment (P) is $373.28. Solve for the payment(P). 1 - 5 * ( ) * * Recall the amortization formula. 3 - 1 Enter the values: P = 300, I = 0.01, N = 60 3 - [...]

  • Page 15

    EL-9650/9600c Graphing Calculator 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. Notes Step & Key Operation *Use either pen touch or cursor to operate. Display 3-2 The Solver mode is used to solve one unknown variable by inputting[...]

  • Page 16

    Step & Key Operation *Use either pen touch or cursor to operate. Display EL-9650/9600c Graphing Calculator Notes The solver feature will graph the left side of the equation (volume, y = 30), then the right side of the equation ( y = 10 r 2 ), and finally will calculate the intersection of the two graphs to find the solution. The radius is 0.98 [...]

  • Page 17

    EL-9650/9600c Graphing Calculator 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. Notes Step & Key Operation *Use either pen touch or cursor to operate. Display 3-3 The Solver mode is used to solve one unknown variable by inputting[...]

  • Page 18

    Step & Key Operation *Use either pen touch or cursor to operate. Display Notes EL-9650/9600c Graphing Calculator 3-3 Enter the values: A = 50, B = 8, C = 10. 3 - 2 Newton's method will prompt with a guess or a starting point. 1 - 5 Solve for the height and enter a starting point of 1. * The answer is : h = 4.17 Solve. 1 - 6 ( ) Save this f[...]

  • Page 19

    EL-9650/9600c Graphing Calculator * * * * G raphing P olynomials and T racing to F ind the R oots A polynomial y = f ( x ) is an expression of the sums of several terms that contain differ ent powers of the same originals. The roots are found at the intersection of the x- axis and the graph, i. e. when y = 0 . Draw a graph of a polynomial and appro[...]

  • Page 20

    Step & Key Operation *Use either pen touch or cursor to operate. Display Notes EL-9650/9600c Graphing Calculator * (repeatedly) Note that the tracer is flashing on the curve and the x and y coordinates are shown at the bottom of the screen. The root is exactly x = 1. (Zooming is not needed to find a better approximate.) Move the tracer near the[...]

  • Page 21

    EL-9650/9600c/9450/9400 Graphing Calculator 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. Setting the zoom factors to 5 : * G raphing P olynomials and J umping to F ind the Roots Draw a graph of a polynomial and find the roots by usi[...]

  • Page 22

    Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) EL-9650/9600c/9450/9400 Graphing Calculator Notes 2 - 4 2 - 3 Find the next root. x 2.05 x 0.24 Find the next root. The calculator allows jumping to find the roots by graphing a polynomial and using the Calculate featur[...]

  • Page 23

    EL-9650/9600c/9450/9400 Graphing Calculator There may be differences in the results of calculations and graph plotting depending on the setting. Return all settings to the default and delete all data. Choose the viewing window “-5 < X < 5”, “-10 < Y < 10” using Rapid window feature * * ( ) * * * * As the T ool feature is only av[...]

  • Page 24

    Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) EL-9650/9600c/9450/9400 Graphing Calculator Notes Access the Tool menu. Select the number of variables. Enter the system of equations. Using the system function, it is possible to solve simulta- neous linear equations. [...]

  • Page 25

    EL-9650/9600c Graphing Calculator 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. Notes Step & Key Operation *Use either pen touch or cursor to operate. Display Enter ing and M ultiplying M atrices 1. Enter a 3 x 3 matrix A 2. Ente[...]

  • Page 26

    Step & Key Operation *Use either pen touch or cursor to operate. Display Notes EL-9650/9600c Graphing Calculator Matrix multiplication can be performed if the number of col- umns of the first matrix is equal to the number of rows of the second matrix. The sum of these multiplications (1 . 1 + 2 . 4 + 1 . 7) is placed in the 1,1 (first row, firs[...]

  • Page 27

    EL-9650/9600c Graphing Calculator 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. Notes Step & Key Operation *Use either pen touch or cursor to operate. Display 1. Enter the 3 x 3 identity matrix in matrix A. 2. Find the inverse ma[...]

  • Page 28

    Step & Key Operation *Use either pen touch or cursor to operate. Display Notes EL-9650/9600c Graphing Calculator 3 - 3 3 - 1 Delete the input matrices for future use. The 1 is the x coordinate, the 2 the y coordinate, and the 3 the z coordinate of the solution point. ( x , y , z )=(1, 2, 3) The system of equations can be expressed as Enter the [...]

  • Page 29

    EL-9650/9600c Graphing Calculator S olving I nequalities T o solve an inequality, expressed by the form of f ( x ) ≤ 0, f ( x ) ≥ 0, or form of f ( x ) ≤ g ( x ) , f ( x ) ≥ g ( x ) , means to find all values that make the inequality true. There are two methods of finding these values for one-variable inequalities, using graphical technique[...]

  • Page 30

    Notes Step & Key Operation *Use either pen touch or cursor to operate. Display EL-9650/9600c Graphing Calculator 2 - 1 Enter y = 3(4 - 2 x ) for Y1 and y = 5 - x for Y2. * (7 times) (4 times) * 2 - 2 View the graph. 2 - 3 Access the Set Shade screen. * * 2 - 4 Set up the shading. Since the inequality being solved is Y1 ≥ Y2, the solu- tion is[...]

  • Page 31

    EL-9650/9600c/9450/9400 Graphing Calculator 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. Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) S olvi[...]

  • Page 32

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 4 Move the tracer and find another intersection. y = 2 x - 5 and y = 7 intersect at (6,7). * 5 Solve the inequalities. The solution to the “double” inequality -1 ≤[...]

  • Page 33

    EL-9650/9600c/9450/9400 Graphing Calculator 4 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. Set the zoom to the decimal window: * ( * ) Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to oper[...]

  • Page 34

    EL-9650/9600c/9450/9400 Graphing Calculator 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. Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 7-4 G [...]

  • Page 35

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 7-4 Use the cursor to check the position of each point. (Zoom in as necessary). Points in the solution region are (2.8, -1.4) and (-8, 4). Points outside the solution re[...]

  • Page 36

    EL-9650/9600c Graphing Calculator 8-1 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. Set the zoom to the decimal window: * ( * ) Notes Step & Key Operation *Use either pen touch or cursor to operate. Display S lope and I nter cept[...]

  • Page 37

    Notes Step & Key Operation *Use either pen touch or cursor to operate. Display EL-9650/9600c Graphing Calculator 2 - 3 View the graph. 2 - 5 Change the coefficients to graph y =| x |-1. 2 - 4 View the graph. The EL-9650/9600c shows absolute values with | |, just as written on paper, by using the Equation editor. Use of the calculator allows var[...]

  • Page 38

    EL-9650/9600c/9450/9400 Graphing Calculator 8-2 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. Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) S [...]

  • Page 39

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) y = | x | changes to y = | x -2| 2 - 1 Move the original graph to the right by 2. * * 3 - 1 Access the Change feature. * 2 -2 Save the new graph and look at the relation[...]

  • Page 40

    EL-9650/9600c/9450/9400 Graphing Calculator 8-3 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. Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) S [...]

  • Page 41

    EL-9650/9600c/9450/9400 Graphing Calculator 8-4 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. Set viewing window to “-5< x <50,” and “-10< y <10” using Rapid W indow featur e to solve Q1. * * * Notes Step & Ke[...]

  • Page 42

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 8-4 2 - 1 Enter the function y = |3.5 x + 4|for Y1. Enter y = 10 for Y2. * * * 2 - 2 * * * * * Since the inequality you are solving is Y1 > Y2, the solu- tion is wher[...]

  • Page 43

    EL-9650/9600c/9450/9400 Graphing Calculator 8-5 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. Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) E [...]

  • Page 44

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) = 0.75 , = 0 .75 8-5 2 - 2 Is | x + y | = | x | +| y |? Think about this problem according to the cases when x or y are positive or negative. If x ≥ 0 and y ≥ 0 [e.g[...]

  • Page 45

    EL-9650/9600c/9450/9400 Graphing Calculator 9-1 G raphing Rational F unctions A rational function f ( x ) is defined as the quotient where p ( x ) and q ( x ) are two polynomial functions such that q ( x ) ≠ 0. The domain of any rational function consists of all values of x such that the denominator q ( x ) is not zero. A rational function consis[...]

  • Page 46

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) The y -intercept is at (0 ,1). No- tice that there are no x -inter- cepts for the graph of f ( x ) . 9-1 2 Find the domain and the vertical asymptote of f ( x ), tracing[...]

  • Page 47

    EL-9650/9600c/9450/9400 Graphing Calculator 9-2 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. Set the zoom to the decimal window: * ( * ) * Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to [...]

  • Page 48

    EL-9650/9600c/9450/9400 Graphing Calculator 10-1 The graph of the equation y = √ x+ 2 is the "top half" of the parabola and the graph of the equation y = - √ x + 2 gives the "bottom half." There may be differences in the results of calculations and graph plotting depending on the setting. Return all settings to the default v[...]

  • Page 49

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 2 - 1 Change to parametric mode. * * 2 - 2 Rewrite x = y 2 - 2 in parametric form. Enter X1T = T 2 -2 and Y1T = T. Let y = T and substitute in x = y 2 - 2, to obtain x =[...]

  • Page 50

    EL-9650/9600c/9450/9400 Graphing Calculator 10-2 Solve the equation for y. Enter y = √ 4 - x 2 for Y1 (the top half). Enter y = - √ 4 - x 2 for Y2. x 2 - 2 x + y 2 + 4 y = 2 x 2 - 2 x+y 2 + 4 y+ 4 = 2 + 4 x 2 - 2 x + ( y+ 2) 2 = 6 ( y+ 2) 2 = 6 -x 2 + 2 x y+ 2 = ± √ 6 -x 2 + 2 x y = ± √ 6 -x 2 + 2 x - 2 There may be differences in the res[...]

  • Page 51

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 2 - 2 * * * * * Enter y = √ 6 - x 2 + 2 x for Y1, y = Y1 - 2 for Y2, and y = -Y1 -2 for Y3. Notice that if you enter y = √ 6 - x 2 + 2 x - 2 for Y1 and y = - Y1 for [...]

  • Page 52

    EL-9650/9600c/9450/9400 Graphing Calculator 10-3 Enter Y1 = √ 3 - 3( x - 3) 2 Y2 = Y1 - 2 Y3 = -Y1 -2 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. Set the zoom to the decimal window: * ( * ) * Notes Step & Key Operation (When [...]

  • Page 53

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 4 Adjust the screen to see the bottom part of the ellipse using the Rapid Zoom feature. * * 3 View the graph. 5 View the graph in the new window. Graphing an ellipse can[...]

  • Page 54

    EL-9650/9600c/9450/9400 Graphing Calculator 10-4 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. Set the zoom to the decimal window: * ( * ) * Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to[...]

  • Page 55

    EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Display (When using EL-9650/9600c) 3 View the graph. 4 Zoom out the screen. * * Graphing hyperbolas can be perfor med easily on the calculator display. In addition to the Zoom-in/Zoom-out features, the EL[...]

  • Page 56

    Graphing keys Power supply ON/OFF key Alphabet specification key Secondary function specification key Display screen Cursor movement keys Clear/Quit key Variable enter key Calculation execute key Communication port for peripheral devices K ey pad for the SHARP EL-9650/9600c C alculator Vol.1 Front.Back.layout.p65 02.10.28, 1:14 PM Page 5 Adobe Page[...]

  • Page 57

    Graphing keys Power supply ON/OFF key Alphabet specification key Secondary function specification key Display screen Cursor movement keys Clear/Quit key Variable enter key Calculation execute key Communication port for peripheral devices K ey pad for the SHARP EL-9450/9400 Calculator Vol.1 Front.Back.layout.p65 02.10.28, 1:14 PM Page 6 Adobe PageMa[...]

  • Page 58

    Dear Sir/Madam W e would like to take this opportunity to invite you to create a mathematical problem which can be solved with the SHARP graphing calculator EL-9650/9600c/9450/9400. For this purpose, we would be grateful if you would complete the form below and return it to us by fax or mail, specifying which calculator you are writing problems for[...]

  • Page 59

    SHARP CORPORA TION Osaka, J apan Fax: BEFORE ST ARTING : W rite any conditions to be set up before solving the problems. STEP NOTES SHARP Graphing Calculator Vol.1 Insert.layout.p65 02.10.28, 1:14 PM 2[...]

  • Page 60

    SHARP CORPORA TION OSAKA, JAPAN Vol.1 Front.Back.layout.p65 02.10.28, 1:14 PM Page 7 Adobe PageMaker 6.5J/PPC[...]