2x2 - x - 4y + 3 = 0
-4y = -2x2 = x - 3
y = (1/2)x2 - (1/4)x + (3/4)

This is a parabola which opens upward.  The vertex is located where 
x = (-1/4)/(2[1/2]) = 1/4.  If x = 1/4, then y = 23/32.  Thus, the vertex is 
at (1/4, 23/32).  

y2 + x + 3y - 2 = 0
x = -y2 - 3y + 2  (note you could solve for y and end up with a 
                        square root of a large expression also)
This is a parabola which opens to the left (since the coefficient of 
y2 in the standard form is negative) and has it's vertex where 
y = -(-3)/(-2).  If y = -3/2, then x = 17/4.  Thus, the vertex is at 
(17/4, -3/2).  The graph is shown below.

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