Whenever I'm doing a question on curves, and I am given the equation without the graph I can reasonably visualise in my head what that graph would look like, and for the more complicated equations, I can just put some values in and figure it out.

However, I can't do this for parametric equations and it puts me off answering the question if I don't know what the graph would look like. if given a parametric equation in the form:

$x = f(t)$

$y = g(t)$

How can i tell what the graph would look like without having to start messing on with plotting points or algebraic manipulation, it doesn't have to be exact, just the generalised shape, (i.e. is it a circle? in what quadrant? Is it a quadratic curve? u or n? Is it a trigonometric graph?) and stuff like that so I can get a general idea for what I'm dealing with. thanks in advance. (this is for A-level questions if that helps at all)

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    $\begingroup$ You can consider the roots and extrema of those functions. On a side note, no idea why you were downvoted. You should however aim to reason about curves even without a graph. $\endgroup$ – lightxbulb Feb 7 at 12:14
  • $\begingroup$ Try using the free program GeoGebra (www.geogebra.org) to plot parametric curves and get a feel for them. Type (cos(x), sin(x)) into the input line for example. $\endgroup$ – Paul Feb 7 at 12:43
  • $\begingroup$ I can't exactly whip out my phone in the middle of an exam, also thanks for the advice about the roots and extremes. $\endgroup$ – aidan Feb 7 at 14:09
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    $\begingroup$ Obviously, you would gain some insight into parametric curves before the exam. Perhaps you could change your question to make it clear you are only talking about what you might do in the middle of an exam? $\endgroup$ – Paul Feb 8 at 9:56
  • $\begingroup$ en.wikipedia.org/wiki/Curve_sketching $\endgroup$ – Adam Feb 12 at 20:48

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