I know this isn't an answer but it's far too long for a comment. There's a problem with your SQL, caused by the LEFT OUTER JOIN; you're counting questions multiple times so the problem is both slightly better and slightly worse than what you think.

I also disagree with your definition of a "good" answer. By definition an accepted answer is "good" as it has helped the OP (unless of course they've been pushed into accepting it by loads of comments but that's another matter). I've excluded Community owned questions and answers as I don't really think they are relevant (and it helps the query to work!).

Your first set of results on the [number of open questions by quarter][1] now returns the following:
<pre>
Year Quarter Questions Answered GoodAnswer 
---- ------- --------- -------- ---------- 
2008 3       18142     99.98%   99.78%     
2008 4       39557     99.85%   97.89%     
2009 1       54286     99.71%   95.96%     
2009 2       76133     99.51%   93.85%     
2009 3       99291     99.18%   91.91%     
2009 4       114135    98.97%   91.02%     
2010 1       144028    98.56%   89.97%     
2010 2       160493    97.91%   87.36%     
2010 3       188612    97.41%   86.03%     
2010 4       207395    97.23%   85.47%     
2011 1       269672    96.71%   84.21%     
2011 2       301200    95.34%   82.10%     
2011 3       335106    88.66%   75.21%     
2011 4       339592    87.62%   73.92%     
2012 1       409490    85.61%   70.71%     
2012 2       419391    81.33%   64.74%    </pre>

As you can see the percentage of answered questions is a little worse than you thought, but the percentage of questions with a "good" answer is a little better. Personally I think the telling point here is not necessarily the number of questions but where the differences lie between my results and your own. For Q4 2008 you have 122,616 and I've got 39,557 questions, which implies that every question received over 3 answers. For Q2 2012 the difference is minimal, on average questions receiving about 1.2 answers.

I've also run this for [questions with a score >= 0][2]:

<pre>
Year Quarter Questions Answered GoodAnswer 
---- ------- --------- -------- ---------- 
2008 3       18084     99.98%   99.78%     
2008 4       39374     99.85%   97.91%     
2009 1       53930     99.71%   95.98%     
2009 2       75565     99.51%   93.86%     
2009 3       98411     99.18%   91.94%     
2009 4       112677    98.96%   91.06%     
2010 1       142475    98.54%   90.03%     
2010 2       158929    97.90%   87.39%     
2010 3       186719    97.38%   86.04%     
2010 4       205092    97.20%   85.52%     
2011 1       266760    96.68%   84.26%     
2011 2       296514    95.27%   82.13%     
2011 3       327715    88.40%   75.11%     
2011 4       330472    87.28%   73.74%     
2012 1       395629    85.10%   70.48%     
2012 2       402573    81.11%   64.78%     </pre>

I think the surprise here is how little difference it makes. It reflects well on Stack Overflow that no matter if the question is not as good as it could be you are just as likely to get a "good" answer. Obviously, closed questions would skew this massively and as a number of "poor" questions get closed not too much can be read into this.

Lastly, here the same query is for [questions with a score >= 1][3]:

<pre>
Year Quarter Questions Answered GoodAnswer 
---- ------- --------- -------- ---------- 
2008 3       16312     99.98%   99.83%     
2008 4       33304     99.88%   98.81%     
2009 1       41506     99.76%   98.12%     
2009 2       53316     99.70%   97.33%     
2009 3       64491     99.53%   96.49%     
2009 4       67875     99.30%   95.56%     
2010 1       97743     98.97%   94.19%     
2010 2       101814    98.41%   92.33%     
2010 3       113190    97.94%   91.29%     
2010 4       118231    97.81%   90.87%     
2011 1       146083    97.48%   90.11%     
2011 2       161480    96.51%   88.55%     
2011 3       158318    95.30%   86.54%     
2011 4       154275    94.38%   85.07%     
2012 1       166750    93.16%   83.35%     
2012 2       150147    91.25%   80.49% </pre>

As you can see the number of answered questions and the number of questions answered "well" significantly improves though the same drop-off is observable.

My own conclusion from these statistics is that a finesse to the system to remove unanswered questions, or whatever it might be, is not what is required. The number of answered "good" questions at over 91% is, in my opinion, a pretty high number.

What seems to be needed is an increase in the number of people who answer questions. Whilst Stack Overflow has had an ever increasing number of people _asking_ questions there hasn't been a commensurate increase in the number of people answering them.

I ran a [little query][4] to test this hypothesis:

<pre>
Year Quarter Questioning Answering 
---- ------- ----------- --------- 
2008 3       6451        9091      
2008 4       10755       13366     
2009 1       13739       16085     
2009 2       18966       21351     
2009 3       24511       25774     
2009 4       37479       36660     
2010 1       47564       42199     
2010 2       57072       47838     
2010 3       66546       53524     
2010 4       73404       61090     
2011 1       95670       76315     
2011 2       109801      79702     
2011 3       127506      86461     
2011 4       125765      90960     
2012 1       152582      109684    
2012 2       164801      114608   </pre>

As you can see in the "early" days the number of users answering questions was more than the number of people asking them. This has now been completely reversed and the questioners are in the ascendant.

What the solution is, I'm not entirely sure. What seems certain though is that Stack Overflow needs to find a way of converting question _askers_ into question _answerers_. Without flooding the place with crap answers.

  [1]: http://data.stackexchange.com/stackoverflow/query/76989/percentage-of-open-questions-with-answers-by-quarter
  [2]: http://data.stackexchange.com/stackoverflow/query/76988/percentage-of-open-questions-with-answers-by-quarter
  [3]: http://data.stackexchange.com/stackoverflow/query/76997/percentage-of-open-questions-with-answers-by-quarter
  [4]: http://data.stackexchange.com/stackoverflow/query/76996/number-of-users-answering-or-questioning