WRITING EQUATIONS FOR PICTURES

Technology Assessing Mathematics Students

M. Freeman, J. Geoghagan

2007

 

  1. Create a picture using computer graphics, or by drawing.  Your sketch must include, but is not limited to a square root function, line segments of different slopes, parabolas, circles, and ellipses, as well as shading created from inequalities.  It may include a hyperbola  as well.  Either import your picture on Geometer Sketchpad, position it on a grid, scale it to fit the page and print it, or hand draw your picture on a sheet of graph paper. Label your coordinate system all the way across and up either before or after printing to indicate your scale.  (DUE DATE: March 30 )
  2. Determine the equations/inequalities for all parts of the picture.  Include the domain and range of each equation.  Neatly list/type the equations in standard form (or slope-intercept form for lines) under appropriate headings and provide corresponding indicators on the sketch.
  3. Write a step by step program so that someone else could duplicate your picture with or without a calculator. Provide a printout of the calculator program.
  4. For an extra grade, create a colorful poster that contains your original grid form of the picture, a copy of the calculator picture and the program.  (Extra quiz grade or 5 extra credit points.)

 

 

TIMELINE:----DUE DATES:

1.  Drawing:                      Due March 30

2.  List of equations (#2)  Due  April 17 (about 10 days later)

3.  Program                       Due May 4 (one month later)

 

STANDARD FORM FOR EQUATIONS NOT STUDIED YET:

 

Circle:       x2+y2=r2                      (Center – (0,0), radius = r)

                  (x-h)2+(y-k)2=r2              (Center – (h,k), radius = r)

 

Ellipse:                        Center – (0,0); a & b give the length of the major & minor axes

                    Center – (h,k); a & b give the length of the major & minor axes

 

Hyperbola:                  Center- (0,0), asymptotes:

                     Center – (h,k);  asymptotes:

Parabola:             Vertex: (h,k), a determines how narrow/wide it is

Square Root: y =       Vertical & horizontal transformation:  x=a, y = b