Sharp EL-9650 Handbook

Graphing calculator algebra
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Graphing Calculator
EL-9650/9600c/9450/9400
Handbook Vol. 1
Algebra
EL-9650
EL-9450

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Table of Contents
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Summary of Contents for Sharp EL-9650

  • Page 1 Graphing Calculator EL-9650/9600c/9450/9400 Handbook Vol. 1 Algebra EL-9650 EL-9450...
  • Page 2: Table Of Contents

    Contents 1. Linear Equations Slope and Intercept of Linear Equations Parallel and Perpendicular Lines 2. Quadratic Equations Slope and Intercept of Quadratic Equations Shifting a Graph of Quadratic Equations 3. Literal Equations Solving a Literal Equation Using the Equation Method (Amortization) Solving a Literal Equation Using the Graphic Method (Volume of a Cylinder) Solving a Literal Equation Using Newton’s Method (Area of a Trapezoid) 4.
  • Page 3: Read This First

    • Some features are provided only on the EL-9650/9600c and not on the EL-9450/9400. (Substi- tution, Solver, Matrix, Tool etc.) • As this handbook is only an example of how to use the EL-9650/9600c and 9450/9400, please refer to the manual for further details.
  • Page 4 View both graphs. Notice that the addition of 2 moves Before Starting As the Substitution feature is only available on the EL-9650/9600c, this section does not apply to the EL-9450/9400. the basic y =x graph up two units and the addition of -2 moves the...
  • Page 5: Slope And Intercept Of Linear Equations

    EL-9650/9600c/9450/9400 Graphing Calculator Slope and Intercept of Linear Equations 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. We call this equation a linear equation since its graph is a straight line.
  • Page 6 EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation Display (When using EL-9650/9600c) (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Enter the equation y = - x for Y2. X/ /T/ View both graphs. Notice how Y2 decreases...
  • Page 7: Parallel And Perpendicular Lines

    EL-9650/9600c/9450/9400 Graphing Calculator Parallel and Perpendicular Lines Parallel and perpendicular lines can be drawn by changing the slope of the linear equation and the y intercept. 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.
  • Page 8 EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation Display (When using EL-9650/9600c) (When using EL-9650/9600c) *Use either pen touch or cursor to operate. View the graphs. These lines have slopes that are negative reciprocals of GRAPH each other (m = - ).
  • Page 9: Quadratic Equations

    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) + k, where a is the coefficient of the second degree term (y = ax + bx + c) and (h, k) is the vertex of the parabola formed by the quadratic equation.
  • Page 10 (reflect it) across the x-axis. The EL-9650/9600c 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,...
  • Page 11: Shifting A Graph Of Quadratic Equations

    EL-9650/9600c/9450/9400 Graphing Calculator Shifting a Graph of Quadratic Equations A quadratic equation of y in terms of x can be expressed by the standard form y = a (x - h) + k, where a is the coefficient of the second degree term (y = ax + bx + c) and (h, k) is the vertex of the parabola formed by the quadratic equation.
  • Page 12 ALPHA form y = a (x - h) + k and broadening the graph is equivalent to decreasing an a (<1). The Shift/Change feature of the EL-9650/9600c/9450/9400 allows visual understanding of how graph changes affect the form of quadratic equations.
  • Page 13: Solving A Literal Equation Using The Equation Method (Amortization)

    EL-9650/9600c Graphing Calculator Solving a Literal Equation Using the Equation Method (Amortization) The Solver mode is used to solve one unknown variable by inputting known variables, by three methods: Equation, Newton’s, and Graphic. The Equation method is used when an exact solution can be found by simple substitution.
  • Page 14 $17550.28. 2nd F With the Equation Editor, the EL-9650/9600c 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 the Solver mode when using the EL-9650/9600c.
  • Page 15: Solving A Literal Equation Using The Graphic Method (Volume Of A Cylinder)

    EL-9650/9600c Graphing Calculator Solving a Literal Equation Using the Graphic Method (Volume of a Cylinder) The Solver mode is used to solve one unknown variable by inputting known variables. There are three methods: Equation, Newton’s, and Graphic. The Equation method is used when an exact solution can be found by simple substitution.
  • Page 16 EL-9650/9600c Graphing Calculator Notes Step & Key Operation Display *Use either pen touch or cursor to operate. Set the variable range from 0 to 2. The graphic solver will prompt with a variable range for solv- ENTER ENTER ing. <3 r =1 = 1 <3...
  • Page 17: Solving A Literal Equation Using Newton's Method (Area Of A Trapezoid)

    EL-9650/9600c Graphing Calculator Solving a Literal Equation Using Newton's Method (Area of a Trapezoid) The Solver mode is used to solve one unknown variable by inputting known variables. There are three methods: Equation, Newton’s, and Graphic. The Newton’s method can be used for more complicated equations.
  • Page 18 EL-9650/9600c Graphing Calculator Notes Step & Key Operation Display *Use either pen touch or cursor to operate. Newton's method will Solve for the height and enter a starting point of 1. prompt with a guess or a starting point. 2nd F ENTER The answer is : h = 4.17...
  • Page 19: Graphing Polynomials And Tracing To Find The Roots

    EL-9650/9600c Graphing Calculator Graphing Polynomials and Tracing to Find the Roots A polynomial y = f (x) is an expression of the sums of several terms that contain different powers of the same originals. The roots are found at the intersection of the x-axis and the graph, i.
  • Page 20 EL-9650/9600c Graphing Calculator Notes Step & Key Operation Display *Use either pen touch or cursor to operate. Tracer Note that the tracer is flashing Move the tracer near the left-hand on the curve and the x and y root. coordinates are shown at the bottom of the screen.
  • Page 21: Graphing Polynomials And Jumping To Find The Roots

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Polynomials and Jumping to Find the Roots A polynomial y = f (x) is an expression of the sums of several terms that contain different powers of the same originals. The roots are found at the intersection of the x- axis and the graph, i.
  • Page 22 EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation Display (When using EL-9650/9600c) (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Find the next root. 0.24 2nd F CALC Find the next root. 2.05 2nd F CALC The calculator allows jumping to find the roots by graphing a polynomial...
  • Page 23: Solving A System Of Equations By Graphing Or Tool Feature

    Choose the viewing window “-5 < X < 5”, “-10 < Y < 10” using Rapid window feature ENTER ALPHA ENTER ENTER WINDOW As the Tool feature is only available on the EL-9650/9600c, the example 2 does not apply to the EL-9450/9400. Step & Key Operation Display Notes (When using EL-9650/9600c) (When using EL-9650/9600c) *Use either pen touch or cursor to operate.
  • Page 24 EL-9650/9600c/9450/9400 Graphing Calculator Notes Step & Key Operation Display (When using EL-9650/9600c) (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Access the Tool menu. Select the Using the system function, it number of variables. is possible to solve simulta- neous linear equations.
  • Page 25: Entering And Multiplying Matrices

    EL-9650/9600c Graphing Calculator Entering and Multiplying Matrices 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 linear equations with multiple variables. Example Enter two matrices and execute multiplication of the two.
  • Page 26 EL-9650/9600c Graphing Calculator Notes Step & Key Operation Display *Use either pen touch or cursor to operate. Enter a 3 x 3 matrix B. MATRIX ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER Matrix multiplication can be Multiply the matrices A and B together at the home screen.
  • Page 27: Solving A System Of Linear Equations Using Matrices

    EL-9650/9600c Graphing Calculator Solving a System of Linear Equations Using Matrices 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.
  • Page 28 EL-9650/9600c Graphing Calculator Notes Step & Key Operation Display *Use either pen touch or cursor to operate. Enter a 3 x 3 matrix B. ENTER MATRIX ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER ENTER Some square matrices have no...
  • Page 29: Solving Inequalities

    EL-9650/9600c Graphing Calculator Solving Inequalities To 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.
  • Page 30 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-9650/9600c allows the solution region to be indicated visually using the Shade feature. Also, the points of intersection can be obtained easily.
  • Page 31: Solving Double Inequalities

    EL-9650/9600c/9450/9400 Graphing Calculator Solving Double Inequalities The solution to a system of two inequalities in one variable consists of all values of the variable that make each inequality in the system true. A system f (x) a, f (x) b, where the same expression appears on both inequalities, is commonly referred to as a “double”...
  • Page 32 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-9650/9600c/9450/9400 allows the solution region to be indicated visually using the Shade feature. Also, the points of intersection can be obtained easily.
  • Page 33: System Of Two-Variable Inequalities

    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-9650/9600c/9450/9400 allows the solution region to be indicated visually using the Shade feature. Also, the points of intersection can be obtained easily.
  • Page 34: Graphing Solution Region Of Inequalities

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Solution Region of Inequalities The solution region of an inequality consists of all points (a, b) such that when x = a, and y = b, all inequalities are true. Example Check to see if given points are in the solution region of a system of inequalities.
  • Page 35 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. The EL-9650/9600c/9450/9400 allows the solution region to be indicated visually using the Shading feature. Also, the free-moving tracer or Zoom-in feature will allow the...
  • Page 36: Slope And Intercept Of Absolute Value Functions

    EL-9650/9600c Graphing Calculator Slope and Intercept of Absolute Value Functions The absolute value of a real number x is defined by the following: |x| = x if x -x if x If n is a positive number, there are two solutions to the equation |f (x)| = n because there are exactly two numbers with the absolute value equal to n: n and -n.
  • Page 37 The EL-9650/9600c 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...
  • Page 38: Shifting A Graph Of Absolute Value Functions

    EL-9650/9600c/9450/9400 Graphing Calculator Shifting a graph of Absolute Value Functions The absolute value of a real number x is defined by the following: |x| = x if x -x if x If n is a positive number, there are two solutions to the equation |f (x)| = n because there are exactly two numbers with the absolute value equal to n: n and -n.
  • Page 39 ALPHA EL-9650/9600c/9450/9400 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.
  • Page 40: Solving Absolute Value Equations

    = |5x - 4| - 6. The EL-9650/9600c/9450/9400 shows absolute values with | |, just as written on paper, by using the Equation editor. The graphing feature of the calculator shows the solution of the absolute value function visually.
  • Page 41: Solving Absolute Value Inequalities

    EL-9650/9600c/9450/9400 Graphing Calculator Solving Absolute Value Inequalities To solve an inequality means to find all values that make the inequality true. Absolute value inequalities are of the form |f (x)|< k, |f (x)| k, |f (x)|> k, or |f (x)| k. The graphical solution to an absolute value inequality is found using the same methods as for normal inequalities.
  • Page 42 The EL-9650/9600c/9450/9400 shows absolute values with | |, just as written on paper, by using the Equation editor. 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.
  • Page 43: Evaluating Absolute Value Functions

    EL-9650/9600c/9450/9400 Graphing Calculator Evaluating Absolute Value Functions The absolute value of a real number x is defined by the following: |x| = x if x -x if x Note that the effect of taking the absolute value 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.
  • Page 44 |x /y| = |x| / |y| The statement is true for all y The EL-9650/9600c/9450/9400 shows absolute values with | |, just as written on paper, by using the Equation editor. The nature of arithmetic of the absolute value can be learned through arithmetical operations of absolute value functions.
  • Page 45: Graphing Rational Functions

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Rational Functions p (x) A rational function f (x) is defined as the quotient where p (x) and q (x) are two q (x) 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.
  • Page 46 Estimate the horizontal asymptote horizontal asymptote of f (x). of f (x). The graphing feature of the EL-9650/9600c/9450/9400 can create the branches of a rational function separated by vertical asymptote. The calculator allows the points of intersection to be obtained easily.
  • Page 47: Solving Rational Function Inequalities

    -1.3 or Do this four times 2nd F CALC -0.8 0.8 or x 1.3. The EL-9650/9600c/9450/9400 allows the solution region of inequalities to be indicated visually using the Shade feature. Also, the points of intersections can be obtained easily.
  • Page 48: Graphing Parabolas

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Parabolas The graphs of quadratic equations (y = ax + bx + c) are called parabolas. Sometimes the quadratic equation takes on the form of x = ay + by + c. 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 must be in terms of x, not y.
  • Page 49 EL-9650/9600c/9450/9400 Graphing Calculator Step & Key Operation Display Notes (When using EL-9650/9600c) (When using EL-9650/9600c) *Use either pen touch or cursor to operate. Change to parametric mode. 2nd F SET UP Rewrite x = y -2 in parametric form. Let y = T and substitute in x Enter X1T = T -2 and Y1T = T.
  • Page 50: Graphing Circles

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Circles The standard equation of a circle of radius r that is centered at a point (h, k) is (x - h) (y - k) . 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.
  • Page 51 ENTER ENTER View the graph in the new window. GRAPH Graphing circles can be performed easily on the calculator display. Also, the Rapid Zoom feature of the EL-9650/9600c/9450/9400 allows shifting and adjusting display area (window) of a graph easily. 10-2...
  • Page 52: Graphing Ellipses

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Ellipses The standard equation for an ellipse whose center is at the point (h, k) with major and (x - h) (y - k) 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.
  • Page 53 ENTER View the graph in the new window. GRAPH Graphing an ellipse can be performed easily on the calculator display. In addition to the Zoom-in/Zoom-out features, the EL-9650/9600c/9450/9400 have the Rapid Zoom feature to adjust the display easily. 10-3...
  • Page 54: Graphing Hyperbolas

    EL-9650/9600c/9450/9400 Graphing Calculator Graphing Hyperbolas The standard equation for a hyperbola can take one of two forms: ( y - k ) ( x - h ) = 1 with vertices at ( h a, k ) or ( y - h)
  • Page 55 ZOOM Graphing hyperbolas can be performed easily on the calculator display. In addition to the Zoom-in/Zoom-out features, the EL-9650/9600c/9450/9400 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.)
  • Page 56 Key pad for the SHARP EL-9650/9600c Calculator Cursor movement keys Graphing keys Clear/Quit key Power supply ON/OFF key Variable enter key Alphabet specification key Calculation execute key Secondary function specification key Communication port for peripheral devices Display screen...
  • Page 57 Key pad for the SHARP EL-9450/9400 Calculator Cursor movement keys Graphing keys Clear/Quit key Power supply ON/OFF key Variable enter key Alphabet specification key Calculation execute key Secondary function specification key Communication port for peripheral devices Display screen...
  • Page 58 EL-9650/9600c or 9450/9400. If your contribution is chosen, your name will be included in the next edition of The EL-9650/9600c/9450/ 9400 Graphing Calculator Handbook. We regret that we are unable to return contributions.
  • Page 59 BEFORE STARTING : Write any conditions to be set up before solving the problems. STEP NOTES SHARP CORPORATION Osaka, Japan Fax: SHARP Graphing Calculator...
  • Page 60 SHARP CORPORATION OSAKA, JAPAN...

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