The optimization process and recommendations:

1. Avoid Calling Functions With Indexed Columns (query line: 23): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `aAuthor` is indexed, the index won’t be used as it’s wrapped with the function `Contains`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
2. Avoid Calling Functions With Indexed Columns (query line: 23): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `aBody` is indexed, the index won’t be used as it’s wrapped with the function `Contains`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
3. Avoid Calling Functions With Indexed Columns (query line: 23): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `aHeadline` is indexed, the index won’t be used as it’s wrapped with the function `Contains`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
4. Avoid Calling Functions With Indexed Columns (query line: 23): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `aSubhead` is indexed, the index won’t be used as it’s wrapped with the function `Contains`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
5. Avoid Calling Functions With Indexed Columns (query line: 23): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index. For example, if the column `aSummary` is indexed, the index won’t be used as it’s wrapped with the function `Contains`. If you can’t find an alternative condition that won’t use a function call, a possible solution is to store the required value in a new indexed column.
6. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

ALTER TABLE `articles` ADD INDEX `articles_idx_alive_full_story_adate` (`aLive`,`full_story`,`aDate`);

The optimized query:

SELECT
        TOP 50 ROW_NUMBER() OVER (ORDER 
    BY
        articles.aDate DESC) AS Row,
        articles.aID,
        articles.aHeadline,
        articles.aAuthor,
        articles.aDate,
        articles.TopStory,
        articles.SiteSectionID,
        articles.PrintSection,
        articles.aSummary,
        articles.small_image,
        articles.aBody 
    FROM
        articles 
    WHERE
        articles.aLive = -1 
        AND articles.full_story = -1 
        AND articles.aDate >= '9/3/2012' 
        AND articles.aDate <= '10/3/2012' 
        AND (
            Contains((articles.aAuthor, articles.aBody, articles.aHeadline, articles.aSubhead, articles.aSummary), '"kodak"')
        ) 
    ORDER BY
        articles.aDate DESC