Sharp EL-9400 Handbook Download

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Graphing Calculator

EL-9600/9400

Handbook Vol. 1

Algebra

EL-9600

EL-9400

HB.Intro

98.10.1, 11:45 AM

Summary of Contents for EL-9400

Page 1: ...Graphing Calculator EL 9600 9400 Handbook Vol 1 Algebra EL 9600 EL 9400 ...

Page 2: ...ations and remove error displays to cancel previous function 3 Initial settings Initial settings are as follows Set up Rad FloatPt 9 Rect Decimal Real Equation Format RectCoord OFF OFF Connect Sequen Stat Plot 2 PlotOFF Shade 2 INITIAL Zoom 5 Default Period 1 PmtEnd Note returns to the default setting in the following operation 4 Using the keys Press to use secondary functions in yellow To select ...

Page 3: ... EL 9600 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 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 EL 9600 Graphing Calculator Slope ...

Page 4: ...ving a System of Equations by Graphing or Tool Feature 6 Matrix Solutions 6 1 Entering and Multiplying Matrices 6 2 Solving a System of Linear Equations Using Matrices 7 Inequalities 7 1 Solving Inequalities 7 2 Solving Double Inequalities 7 3 System of Two Variable Inequalities 7 4 Graphing Solution Region of Inequalities 8 Absolute Value Functions Equations Inequalities 8 1 Slope and Intercept o...

Page 5: ...1 x is dis played first followed by the equation Y2 2x Notice how Y2 becomes steeper or climbs faster Increase the size of the slope m 1 to make the line steeper 1 Graph the equations y x and y 2x 2 Graph the equations y x and y x 3 Graph the equations y x and y x 4 Graph the equations y x and y x 2 Enter the equation y x for Y1 and y 2x for Y2 View both graphs 1 1 Draw graphs of two equations by ...

Page 6: ...down from left to right instead of increasing going up from left to right Negative slopes m 0 make the line decrease or go down from left to right Adding 2 will shift the y x graph upwards View both graphs Enter the equation y x 2 for Y2 3 1 3 2 4 1 4 2 Making a graph is easy and quick comparison of several graphs will help students understand the characteristics of linear equations 1 1 CL GRAPH G...

Page 7: ... A linear equation of y in terms of x can be expressed by the slope intercept form y mx b where m is the slope and b is the y intercept Parallel lines have an equal slope with different y intercepts Perpendicular lines have slopes that are negative reciprocals of each other m These characteristics can be verified by graphing these lines Notes Step Key Operation When using EL 9600 Use either pen to...

Page 8: ...tor 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 form four equal angles 2 2 The Graphing Calculators can be used to draw parallel or perpendicular lines while learning the slope or y intercept of linear equations 1 m GRAPH ...

Page 9: ... value or to delete all data As Substitution feature is only available on the EL 9600 this section does not apply to the EL 9400 Before Start Graph various quadratic equations and check the relation between the graphs and the values of coefficients of the equations Example 1 Graph y x2 and y x 2 2 2 Graph y x2 and y x 2 2 3 Graph y x2 and y 2x 2 4 Graph y x 2 and y 2x 2 1 1 Enter the equation y x ...

Page 10: ... 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 2x2 Notice that the multiplication of 2 pinches or closes the basic y x2 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...

Page 11: ...calculator let the x variable be represented by the horizontal axis and let y be represented by the vertical axis The relation of an equation and its graph can be seen by moving the graph and checking the coefficients of the equation Move or pinch a graph of quadratic equation y x2 to verify the relation between the coefficients of the equation and the graph Example 1 Shift the graph y x 2 upward ...

Page 12: ... Shift Change feature of the EL 9600 9400 allows visual understanding of how graph changes affect the form of quadratic equations 2 2 Save the new graph and observe the changes in the graph and the equation Notice that movement of the basic y x2 graph to the right by 3 units in the direction of the x axis is equivalent to the addition of 3 to the x intercept This demonstrates that movement of the ...

Page 13: ... simple substitution 1 Find the monthly payment on a 15 000 car loan made at 9 interest over four years 48 months using the Equation method 2 Save the formula as AMORT 3 Find amount of loan possible at 7 interest over 60 months with a 300 payment using the saved formula Solve an amortization formula The solution from various values for known variables can be easily found by giving values to the kn...

Page 14: ...L is 17550 28 Solve for the loan L 3 3 With the Equation Editor the EL 9600 9400 displays equations even complicated ones as they appear in the textbook in easy to understand format Also it is easy to find the solution for unknown variables by recalling a stored equation and giving values to the known variables in Solver mode when using the EL 9600 1 4 Enter the values L 15 000 I 0 09 N 48 2nd F E...

Page 15: ...r multiple solutions are expected use the Graphic method This method plots the left and right sides of the equation and then locates the intersection s Solving a Literal Equation Using the Graphic Method Volume of a Cylinder 1 Find the radius of a cylinder with a volume of 30in3 and a height of 10in using the Graphic method 2 Save the formula as V CYL 3 Find the radius of a cylinder with a volume ...

Page 16: ...ure of the calculator is its ability to store and recall equations The solution from various values for known variables can be easily obtained by recalling an equation which has been stored and giving values to the known variables The Graphic method gives a visual solution by drawing a graph Use the larger of the values to be safe r 1 r2 12 1 3 r 2 r2 22 4 3 Recall the formula Enter the values V 2...

Page 17: ...given Solving a Literal Equation Using Newton s Method Area of a Trapezoid 1 Find the height of a trapezoid with an area of 25in2 and bases of length 5 in and 7 in using Newton s method Set the starting point to 1 2 Save the formula as A TRAP 3 Find the height of a trapezoid with an area of 50in2 with bases of 8 and 10 using the saved formula Set the starting point to 1 Find the height of a trapez...

Page 18: ...a for calculating the area of a trapezoid 3 1 The answer is h 5 56 Solve 3 3 One very useful feature of the calculator is its ability to store and recall equations The solution from various values for known variables can be easily obtained by recalling an equation which has been stored and giving values to the known variables in the Solver mode If a starting point is known Newton s method is usefu...

Page 19: ...fficients 1 1 1 2 Example Return to the equation display screen 1 3 View the graph 1 4 4 1 Notes Step Key Operation Use either pen touch or cursor to operate Display There may be differences in the results of calculations and graph plotting depending on the setting Return all settings to the default value or to delete all data Set the zoom to the decimal window Setting the zoom factors to 5 As Sub...

Page 20: ...Zoom in on the left hand root 2 2 Move the tracer to approximate the root 2 3 Return to the previous decimal viewing window 3 1 Move the tracer to approximate the middle root 3 2 Move the tracer near the right hand root Zoom in and move the tracer to find a better approximate 4 The calculator allows the roots to be found or approximated visually by graphing a polynomial and using the Zoom in and T...

Page 21: ...ind the four roots one by one Notes Step Key Operation When using EL 9600 Use either pen touch or cursor to operate Display When using EL 9600 Enter the polynomial y x4 x 3 5x2 3x 1 1 1 1 2 View the graph Find the next root x 2 47 Y is almost but not exactly zero Notice that the root found here is an approximate value x 0 82 4 2 A polynomial y f x is an expression of the sums of several terms that...

Page 22: ...splay When using EL 9600 EL 9600 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 feature without tracing the graph 4 2 5 2nd F CALC 5 2nd F CALC ...

Page 23: ... graphs of equations and is useful for solving a system when there are two variables while the Tool feature can solve a linear system up to six variables and six equations Note that the x and y coordi nates are shown at the bot tom of the screen The answer is x 0 41 y 0 83 1 Solve the system using the Calculate feature 2 Solve the system using the Tool feature Enter the system of equations y x2 1 ...

Page 24: ...f variables Enter the system of equations Using system function it is possible to solve simultaneous linear equations Systems up to six variables and six equa tions can be solved Solve the system 2 1 2 2 2 3 5 1 A system of equations can be solved easily by using the Calculate feature or Tool feature x 0 75 y 2 75 2nd F TOOL B EXE 2nd F 2 5 1 1 3 1 5 ENTER ENTER ENTER ENTER ENTER ENTER ...

Page 25: ... 3 x3 matrix B 3 Multiply the matrices A and B Access the matrix menu Set the dimension of the matrix at three rows by three columns 1 1 1 2 Example Enter the elements of the first row the elements of the second row and the elements of the third row 1 3 A matrix is a rectangular array of elements in rows and columns that is treated as a single element A matrix is often used for expressing multiple...

Page 26: ...placed in the 1 1 first row first column position of the re sulting matrix This process is repeated until each row of A has been multiplied by each column of B Enter a 3x 3 matrix B 2 Multiply the matrices A and B together at the home screen 3 1 Delete the input matrices for future use 3 2 6 1 Matrix multiplication can be performed easily by the calculator MATRIX MATRIX MATRIX X B 2 3 3 1 2 3 4 5 ...

Page 27: ...ave the identity matrix in matrix A 1 1 1 2 Confirm that the identity matrix is stored in matrix A 1 3 Each system of three linear equations consists of three variables Equations in more than three variables cannot be graphed on the graphing calculator The solution of the system of equations can be found numerically using the Matrix feature or the System solver in the Tool feature A system of line...

Page 28: ...culating the inverse Exit the matrix editor and find the inverse of the square matrix B 6 2 repeatedly The calculator can execute calculation of inverse matrix and matrix multiplication A system of linear equations can be solved easily using the Matrix feature 0 17 0 83 0 5 0 5 0 5 0 5 0 17 0 17 0 5 B 1 3 2 x y z 1 2 1 2 1 1 1 1 2 8 1 3 Let each matrix B X C BX C B 1 BX B 1 C multiply both sides b...

Page 29: ...ve an inequality in two methods Example 1 Solve 3 4 2x 5 x by rewriting the right hand side of the inequality as 0 2 Solve 3 4 2x 5 x by shading the solution region that makes the inequality true There may be differences in the results of calculations and graph plotting depending on the setting Return all settings to the default value or to delete all data Before Start Notes Step Key Operation Whe...

Page 30: ...region 2 6 Find where the graphs intersect and solve the inequality The point of intersection is 1 4 3 6 Since the shaded region is to the left of x 1 4 the solution to the inequality 3 4 2x 5 x is all values of x such that x 1 4 Graphical solution methods not only offer instructive visualization of the solution process but they can be applied to inequalities that are often difficult to solve alge...

Page 31: ... b where the same expression appears on both inequalities is commonly referred to as a double inequality and is often written in the form a f x b Be certain that both inequality signs are pointing in the same direction and that the double inequality is only used to indicate an expression in x trapped in between two values Also a must be less than or equal to b in the inequality a f x b or b f x a ...

Page 32: ...double inequality 1 2x 5 7 con sists of all values of x in be tween and including 2 and 6 i e x 2 and x 6 The so lution is 2 x 6 7 2 Graphical solution methods not only offer instructive visualization of the solution process but they can be applied to inequalities that are often difficult to solve algebraically The EL 9600 9400 allows the solution region to be indicated visually using the Shade fe...

Page 33: ...cept functions of the form y where y is defined explicitly in terms of x Example Solve a system of two variable inequalities by shading the solution region 2x y 1 x2 y 1 7 3 2 Enter y 1 2x for Y1 and y 1 x2 for Y2 Shade the points of y value so that Y1 y Y2 5 Graph the system and find the intersections The intersections are 0 1 and 2 3 6 Solve the system The solution is 0 x 2 Graphical solution me...

Page 34: ...ch that when x a and y b all inequalities are true Check to see if given points are in the solution region of a system of inequalities Example 1 Graph the solution region of a system of inequalities x 2y 1 x 2 y 4 2 Which of the following points are within the solution region 1 6 1 8 2 5 2 8 1 4 8 4 1 1 Rewrite the inequalities so that the left hand side is y x 2y 1 y x2 y 4 y 4 x 2 1 x 2 1 2 Ente...

Page 35: ...6 2 1 8 2 This does not materialize 2 5 2 2 5 12 2 2 5 1 This does not materialize 2 8 1 4 2 8 2 1 4 0 2 8 2 1 4 6 44 This materializes 8 4 8 2 4 0 8 2 4 68 This materializes Continuing key operations omitted 2 3 Graphical solution methods not only offer instructive visualization of the solution process but they can be applied to inequalities that are often very difficult to solve algebraically Th...

Page 36: ...The existence of two distinct solutions is clear when the equation is solved graphically An absolute value function can be presented as y a x h k The graph moves as the changes of slope a x intercept h and y intercept k Consider various absolute value functions and check the relation between the graphs and the values of coefficients Example 1 Graph y x 2 Graph y x 1 and y x 1 using Rapid Graph fea...

Page 37: ... just as written on paper by using the Equation editor Use of the calculator allows various absolute value functions to be graphed quickly and shows their characteristics in an easy to understand manner Notice that placing an h 0 within the standard form y a x h k will move the graph right h units on the x axis Notice that adding a k 0 within the standard form y a x h k will move the graph up k un...

Page 38: ...s solved graphically An absolute value function can be presented as y a x h k The graph moves as the changes of slope a x intercept h and y intercept k Move and change graphs of absolute value function y x to check the relation between the graphs and the values of coefficients Example 1 Move the graph y x downward by 2 using the Shift feature 2 Move the graph y x to the right by 2 using the Shift ...

Page 39: ...nship of the function and the graph Notice that the coefficient a in the standard form y a x h k takes charge of changing the slope EL 9600 9400 shows absolute values with just as written on paper by using the Equation editor Use of the calculator allows various absolute value functions to be graphed quickly and shows their characteristics in an easy to understand manner The Shift Change feature o...

Page 40: ... of two distinct solutions is clear when the equation is solved graphically Example Solve an absolute value equation 5 4x 6 1 Enter y 5 4x for Y1 Enter y 6 for Y2 2 View the graph There are two points of in tersection of the absolute value graph and the hori zontal line y 6 3 Find the points of intersection of the two graphs and solve The solution to the equation 5 4x 6 consists of the two values ...

Page 41: ...at the right hand side of the inequality is 0 and the left hand side is a function of x The second method involves graphing each side of the inequality as an individual function Solve absolute value inequalities in two methods Example 1 2 Enter y 20 8 for Y1 1 1 Rewrite the equation 20 8 20 8 0 1 3 View the graph and find the x intercepts x 10 y 0 x 23 33333334 y 0 00000006 Note The intersections ...

Page 42: ...lues of x such that x 4 or x 1 7 Note The value of y in the intersection of the two graphs may not appear exactly as 10 as shown in the example due to an error caused by approxi mate calculation Find the points of intersection Solve the inequality The EL 9600 9400 shows absolute values with just as written on paper by using the Equation editor Graphical solution methods not only offer instructive ...

Page 43: ...of a number is to strip away the minus sign if the number is negative and to leave the number unchanged if it is nonnegative Thus x 0 for all values of x Evaluate various absolute value functions Example 1 Evaluate 2 5 1 2 Is 2 7 2 7 Evaluate each side of the equation to check your answer Is x y x y for all real numbers x and y If not when will x y x y 3 Is Evaluate each side of the equation to ch...

Page 44: ...roblem according to the cases when x or y are positive or negative If x 0 and y 0 e g x y 2 7 If x 0 and y 0 e g x y 2 7 If x 0 and y 0 e g x y 2 7 If x 0 and y 0 e g x y 2 7 x y 2 7 2 7 x y 2 7 2 7 x y x y x y 2 7 2 7 x y 2 7 2 7 x y x y x y 2 7 2 7 x y 2 7 2 7 x y x y x y 2 7 2 7 x y 2 7 2 7 x y x y The statement is true for all y 0 The EL 9600 9400 shows absolute values with just as written on ...

Page 45: ...nal function f x if there are any occur at the x values that make the numerator p x but not the denominator q x zero The y intercept occurs at f 0 There may be differences in the results of calculations and graph plotting depending on the setting Return all settings to the default value or to delete all data Set the zoom to the decimal window Before Start Notes Step Key Operation When using EL 960...

Page 46: ...x 1 There is no vertical asymptote where x 1 since this value of x also makes the numera tor zero Next to the coordi nates x 0 9 y 0 52 see that the calculator does not display a value for y at x 1 since 1 is not in the domain of this rational function repeatedly Find the x and y intercepts of f x 3 4 Estimate the horizontal asymptote of f x The line y 0 is very likely a horizontal asymptote of f ...

Page 47: ...e solutions by graphing each side of the inequalities as an individual function Solve a rational inequality Example Solve 2 by graphing each side of the inequality as an individual function 1 Enter y for Y1 Enter y 2 for Y2 2 Set up the shading Since Y1 is the value on the bottom the smaller of the two and Y2 is the function on the top the larger of the two Y1 Y Y2 3 View the graph 4 Find the inte...

Page 48: ...functions entered in the Y list must be in terms of x not y There are however two methods you can use to draw the graph of a parabola Method 1 Consider the top and bottom halves of the parabola as two different parts of the graph because each individually is a function Solve the equation of the parabola for y and enter the two parts that individually are functions in two locations of the Y list Me...

Page 49: ...in x y2 2 to obtain x T 2 2 2 3 View the graph Consider why only half of the parabola is drawn To understand this use Trace fea ture The graph starts at T 0 and increases Since the window setting is T 0 the region T 0 is not drawn in the graph 2 4 Set Tmin to 6 2 5 View the complete parabola The calculator provides two methods for graphing parabolas both of which are easy to perform 10 1 GRAPH GRA...

Page 50: ... k 2 r 2 In order to put an equation in standard form so that you can graph in rectangular mode it is necessary to solve the equation for y You therefore need to use the process of completing the square Graph the circles in rectangular mode Solve the equation for y to put it in the standard form Example 1 Graph x 2 y 2 4 2 Graph x 2 2x y2 4y 2 1 1 2 1 Solve the equation for y completing the square...

Page 51: ...ened You now have the top portion and the bottom portion of the circle in Y2 and Y3 2 4 View the graph 2 5 Adjust the screen to see the bottom part of the circle using the Rapid feature 2 6 View the graph in the new window Graphing circles can be performed easily on the calculator display Also the Rapid Zoom feature of the EL 9600 9400 allows shifting and adjusting display area window of a graph e...

Page 52: ...nt h k with major and minor axes of length a and b is 1 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 an ellipse consider the top and bottom halves of the ellipse as two different ...

Page 53: ...f the ellipse using the Rapid Zoom feature 3 View the graph 5 View the graph in the new window Graphing ellipse can be performed easily on the calculator display In addition to the Zoom in Zoom out features the EL 9600 9400 have the Rapid Zoom feature to adjust the display easily Wait until the graph is dis played after each operation It takes few seconds to graph 10 3 GRAPH GRAPH ENTER EZ ...

Page 54: ...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 So...

Page 55: ... EL 9600 3 View the graph 4 Zoom out the screen Graphing hyperbolas can be performed easily on the calculator display In addition to the Zoom in Zoom out features the EL 9600 9400 have the Rapid Zoom feature to adjust the display easily See the section Graphing Ellipses No 10 3 about how to use the Rapid Zoom feature 10 4 GRAPH A ZOOM 4 ...

Page 56: ...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 Key pad for the SHARP EL 9600 Calculator ...

Page 57: ...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 Key pad for the SHARP EL 9400 Calculator ...

Page 58: ...your contribution is chosen your name will be included in the next edition of The EL 9600 9400 Graphing Calculator Handbook We regret that we are unable to return contributions We thank you for your cooperation in this project Name Mr Ms School College Univ Address Post Code Country Phone Fax E mail You are making this sheet for the EL 9600 EL 9400 SUBJECT Write a title or the subject you are writ...

Page 59: ...SHARP CORPORATION Osaka Japan Fax BEFORE START Write any conditions to be set up before solving the problems STEP NOTES SHARP Graphing Calculator ...

Page 60: ...SHARP CORPORATION OSAKA JAPAN FAX 06 628 1653 ...

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