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). 

Answered by Trishla S. Maths tutor

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