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Mth 518 report grapes_garachico

Aji Garachico
Aji Garachico

GRAPES is software that allows users to draw and manipulate graphs of functions, relations, curves, and other mathematical objects. It has tools for inputting and editing functions and relations, operating on graphs by changing parameters or dragging points, and analyzing functions through tools like the function value window or definite integral window. The document provides examples of using GRAPES to draw and explore properties of linear and quadratic equations, converting between slope-intercept form and general form for lines, and using the quadratic formula to solve quadratic equations.

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GRAPES (GRAph Presentation & Experiment System) Presented by: AJI A. GARACHICO MAEd Elem. Math
GRAPES is a software for drawing the graphs of functions, relations (equation and inequality), and curves described in parametric or polar forms; in addition, it enables you to explore many of their properties.
BASIC STEPS FOR MANIPULATIONS Producing graphs or objects Operating on graphs Appearance of graph Tools for analyzing function Other useful tools Adding caption to a graph or project Other supplemental tools and managing projects
Producing graphs or objects Input and edit function Input and edit relation (equation/inequality) Input and edit inequalities defining regions Input and edit the expression for curves or elementary objects (elementary objects : circle, point, horizontal and vertical lines) Configuration of line and polygon (segment, line, line with arrow, rectangle, angle, line graph, polygon)
Operating on graphs Increase or decrease parameters, and substitute for parameters Drag a point Manipulate an after-image
Appearance of graph Change display area Change window size
Tools for analyzing function Function value window Definite integral window Display coordinate or equation of the selected graph
Other useful tools Change scale Change wallpaper Define user function Marking pen
Adding caption to a graph or project Display or edit Note Use of label
Other supplemental tools and managing projects Print Copy to clipboard Save or successive save of images Initialization of project Default update File processing File association
APPLICATION OF GRAPES
Linear Equations The "General Form" of the equation of a straight line is: Ax + By + C = 0 A or B can be zero, but not both at the same time. The General Form is not always the most useful form, and you may prefer to use: The Slope-Intercept Form of the equation of a straight line: y = mx + b
Example: Convert 4x - 2y - 5 = 0 to Slope- Intercept Form We are heading for y = mx + b Start with 4x - 2y - 5 = 0 Move all except y to the left: -2y = -4x + 5 Divide all by (-2): y = 2x - 5/2 And we are done! (Note: m=2 and b=-5/2)
Mth 518 report grapes_garachico
Quadratic Equations An example of a Quadratic Equation: Quadratic Equations make nice curves, like this one:
Using the Quadratic Formula Just put the values of a, b and c into the Quadratic Formula, and do the calculations. Example: Solve 5x族 + 6x + 1 = 0 Coefficients are: a = 5, b = 6, c = 1 Quadratic Formula: x = [ -b 賊 (b2-4ac) ] / 2a Put in a, b and c: x = [ -6 賊 (62-451) ] / (25)
Solve: x = [ -6 賊 (36-20) ]/10 x = [ -6 賊 (16) ]/10 x = ( -6 賊 4 )/10 x = -0.2 or -1 And we see them on this graph.
Example: Solve 5x族 + 2x + 1 = 0 Coefficients are: a = 5, b = 2, c = 1 Note that The Discriminant is negative: b2 - 4ac = 22 - 451 = -16 Use the Quadratic Formula: x = [ -2 賊 (-16) ] / 10 The square root of -16 is 4i (i is -1, read Imaginary Numbers to find out more) So:x = ( -2 賊 4i )/10
Answer: x = -0.2 賊 0.4i The graph does not cross the x-axis. That is why we ended up with complex numbers. In some ways it is easier: we don't need more calculation, just leave it as -0.2 賊 0.4i.
REFERENCES http://www.criced.tsukuba.ac.jp/grapes/ http://www.mathsisfun.com/algebra/line- equation-general-form.html http://www.mathsisfun.com/algebra/quad ratic-equation.html
Mth 518 report grapes_garachico

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Mth 518 report grapes_garachico

  • 1. GRAPES (GRAph Presentation & Experiment System) Presented by: AJI A. GARACHICO MAEd Elem. Math
  • 2. GRAPES is a software for drawing the graphs of functions, relations (equation and inequality), and curves described in parametric or polar forms; in addition, it enables you to explore many of their properties.
  • 3. BASIC STEPS FOR MANIPULATIONS Producing graphs or objects Operating on graphs Appearance of graph Tools for analyzing function Other useful tools Adding caption to a graph or project Other supplemental tools and managing projects
  • 4. Producing graphs or objects Input and edit function Input and edit relation (equation/inequality) Input and edit inequalities defining regions Input and edit the expression for curves or elementary objects (elementary objects : circle, point, horizontal and vertical lines) Configuration of line and polygon (segment, line, line with arrow, rectangle, angle, line graph, polygon)
  • 5. Operating on graphs Increase or decrease parameters, and substitute for parameters Drag a point Manipulate an after-image
  • 6. Appearance of graph Change display area Change window size
  • 7. Tools for analyzing function Function value window Definite integral window Display coordinate or equation of the selected graph
  • 8. Other useful tools Change scale Change wallpaper Define user function Marking pen
  • 9. Adding caption to a graph or project Display or edit Note Use of label
  • 10. Other supplemental tools and managing projects Print Copy to clipboard Save or successive save of images Initialization of project Default update File processing File association
  • 12. Linear Equations The "General Form" of the equation of a straight line is: Ax + By + C = 0 A or B can be zero, but not both at the same time. The General Form is not always the most useful form, and you may prefer to use: The Slope-Intercept Form of the equation of a straight line: y = mx + b
  • 13. Example: Convert 4x - 2y - 5 = 0 to Slope- Intercept Form We are heading for y = mx + b Start with 4x - 2y - 5 = 0 Move all except y to the left: -2y = -4x + 5 Divide all by (-2): y = 2x - 5/2 And we are done! (Note: m=2 and b=-5/2)
  • 15. Quadratic Equations An example of a Quadratic Equation: Quadratic Equations make nice curves, like this one:
  • 16. Using the Quadratic Formula Just put the values of a, b and c into the Quadratic Formula, and do the calculations. Example: Solve 5x族 + 6x + 1 = 0 Coefficients are: a = 5, b = 6, c = 1 Quadratic Formula: x = [ -b 賊 (b2-4ac) ] / 2a Put in a, b and c: x = [ -6 賊 (62-451) ] / (25)
  • 17. Solve: x = [ -6 賊 (36-20) ]/10 x = [ -6 賊 (16) ]/10 x = ( -6 賊 4 )/10 x = -0.2 or -1 And we see them on this graph.
  • 18. Example: Solve 5x族 + 2x + 1 = 0 Coefficients are: a = 5, b = 2, c = 1 Note that The Discriminant is negative: b2 - 4ac = 22 - 451 = -16 Use the Quadratic Formula: x = [ -2 賊 (-16) ] / 10 The square root of -16 is 4i (i is -1, read Imaginary Numbers to find out more) So:x = ( -2 賊 4i )/10
  • 19. Answer: x = -0.2 賊 0.4i The graph does not cross the x-axis. That is why we ended up with complex numbers. In some ways it is easier: we don't need more calculation, just leave it as -0.2 賊 0.4i.