Preparing the Blank

• 1). Choose the kind of paper to use. There are two kinds to choose from--blank paper and graph paper. Graph paper is simpler to use, since it already has horizontal and vertical lines. It is generally not costly.
  
  
• 2). Decide how much of the paper will be used to draw the graph and how much will be used below it to list points. Draw a horizontal line for x, and a vertical line for y. The lines should cross each other, creating four equal sections. The upper right hand quarter--"quadrant one"--is for positive x and positive y. The upper left "quadrant two" is for negative x and positive y. The lower left "quadrant three" is for negative x and negative y. The lower right hand "quadrant four" is for positive x and negative y.
  
  
• 3). Draw evenly spaced dots on the lines. On the x line from left to right it could be -3, -2, -1, 0, 1, 2, 3--with the zero at the center. On the y line from bottom to top it could be -3, -2, -1, 0, 1, 2, 3--again with the zero at the center. The numbers can be different. This is only an example.
  
  

Graphing the Equation

• 1). Choose an equation to graph--for discussion purposes, y = x**2 - 1 (y = x-squared minus 1) will be used. Some values need to be chosen to draw the graph.
  
  
• 2). Create a list of points by using the equation, supplying values for x, and determining y. Each of these should fall within the numbers drawn on our axes. If we were to choose a value of x = 3, then y would equal 8, which is out of range and unsuitable. Write acceptable results as (x, y). A calculator helps, but is not essential. For this example we choose,
  
  (-2, 3) Found by plugging in x = -2. Then, y = (-2)(-2) - 1 = 3, so y = 3.
  (-3/2, 5/4)
  (-1, 0)
  (-1/2, -3/4)
  (0, -1)
  (1/2, -3/4)
  (1, 0)
  (3/2, 5/4)
  (2, 3)
  
  
• 3). Draw these points on the blank graph form. To do so for the first point (-2, 3), go to the x-axis and find -2. Then going vertically up, look to the right for y = 3. Make sure the point is drawn directly up from the x = -2 location. Doing this for all the points makes a U-shaped drawing called a parabola, with its center, its lowest point, at (0, -1). The upper part of the branches actually goes upward to infinity, even though the highest points chosen for this example were (-2, 3) and (2, 3). Tiny arrow heads drawn at the tops indicate that.