How do you go about sketching a curve when all you are given is the equation?

- First start by examining the equation. Is it in a recognisable form e.g. the equation of a circle/elipse etc.  - If not, is it in the form y = or x = (these are the most common forms)? These are the steps you should follow for most cases:  - first find the y and x intercepts by putting 0 into y to find the x co-ordinates of where it crosses the x axis and do the same for x to find the y intercepts - then find any turning points (stationary points). Do this by differentiating the euation with respect to x and then setting the differential equal to 0 to find the value of the x co-ordinates at the turning points. Plug this into the main equation to find the corresponding y co-ordinates - For more difficult equations it is better to make a table of values by plugging in 6 or so x values into the equation and getting the corresponding y values and then plotting the points (In an actual session I would use an example equation and plot the graph on the whiteboard in stages by following these steps to demonstrate how they are followed in practice).