Maybe you didn't understand that all four of these statements:

1. y is greater than zero

2. y > 0

3. y is positive

4. y is above the x-axis

all say EXACTLY the same thing.

So y can only be greater than zero where the y-axis has positive 
numbers marked on it.  That's because if y were below the x axis,
that is where the y-axis has negative numbers marked on it.

Maybe you didn't unserstand that when we say "y > 0" we mean that
the points on the graph of y = ax^2+bx+c > 0 have all their y-coordinates
positive, and the only points which have their y-coordinates positive
are the points above the x-axis where the numbers marked on the y-axis 
are all positive.

Below is a typical graph of y = ax^2+bx+c > 0.  Notice that the whole graph 
is ABOVE the x-axis. Look at each point that I have marked on it.  Each point 
has an x-coordinate and a y-coordinate. The x-coordinate of the point 
(-4,6) is -4 and the y-coordinate is +6.  The x-coordinate of the point
(2,3) is 2 and the y-coordinate is +3.  

Notice that the y-coordinate of every point on that graph is a POSITIVE
number. That is it is GREATER than 0.  

Even though some of the x-coordinates are negative and some are positive,
and one is 0, that cannot be said about the y-coordinates of those 
points. The y-coordinates of the points on that graph are all positive and
therefore they are all greater than 0.  " > 0" means "greater than 0".

That's because they are ABOVE the x-axis.  Again, "positive" and "greater 
than 0" both mean exactly the same thing.



Edwin