Quadrant I: x positive, y positive.
Quadrant II: x negative, y positive.
Quadrant III: x negative, y negative.
Quadrant II: x positive, y negative.
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2nd - x is -, y is + 4th - x is +, y is -
-1
Keep in mind that this consists of all points where y=x, ignoring the sign. The graph is a pair of lines forming a gigantic 'X', which are y=x and y=-x. The intersection of the big 'X' is at the origin, and all 4 half-lines take off at 45-degree angles and split each quadrant in half.
Third and fourth
The quadrants formed by the x and y axes are numbered anticlockwise from the quadrant in which both coordinates are positive (which is quadrant I). Thus negative x and positive y is in the quadrant II.