How would you draw (freehand, with compass and ruler) a pretty accurate quadratic curve, say \( y = 3x^2\), in the domain \([-20,20]\)?
Would you have to laboriously plot a lot of points corresponding to the domain that we are interested in?
Are there any tricks that we can use? For example, we know how to draw the circle \(x^2 + y^2 = 1 \) using a compass.
How about a cubic curve \( y = 4 x^3 \)? Would any of the same ideas apply?