The geometric representation of an algebraic equation in a cartesian plane is a graph. Our site emphasizes the relative shapes of these graphs (hence our detailed explanations on curve sketching later). However, we will briefly describe the accurate plotting of a graph.

Plot the graph y = x² - 3x + 1

Solution:

1. Calculate a table of values for x and their corresponding y. Give a relatively large range of values, depending on the amount of space you have. Unless the domain is restricted, a range of positive and negative values is advised. Also, the range should include all important points, like the x- and y- intercepts (if any), stationary points, changes in curvature. (These concepts are explained in various parts of our site)

2. Draw the horizontal (x) and vertical (y) axes. Label and axes and origin.

3. Mark all the calculated points on the graph. We say we plot y against x.

4. Draw a smooth curve through all the points. Though freehand drawing is relatively neat considering you have a steady hand, if you have higher standards, there are always flexible curves and French curves to aid in the drawing. These can be found in stationery shops.

The vertical axis need not necessarily be y and the horizontal axis need not necessarily be x. However, it has been convention to do so, unless, of course, the variable that you are given are not x and y, for example, you can plot s against t.