Drawing Areas Between Curves: Tips & Tricks

[sobadin]

I know its a really dumb question and if i reached this far in math i should know but..how do you draw the diagrams for this topic? Like they give you a region in a plane defined by some kind of inequalities such as (x-2y^2 greater than or equal to 0), (1-x- IyI greater than or equal to 0) and tell you draw it...and I am just spaced out drawing circles all over my paper at this point...THE BEGINNING

 

[HallsofIvy]

Do you mean $x- 2y^2\ge 0$ and $1- x- |y|\ge 0$?

Draw graphs of the corresponding equations. $x- 2y^2= 0$ is the same as $x= 2y^2$, a hyperbola with horizontal axis. 1- x- |y|= 0 is the same as x= 1-|y|, a "broken" line or a "V" opening to the right. Then take one point on each side of the curve to decide which side is "$\ge$" and which is "$\le$.