It depends on how you have your search setup really.
At the page level if you are using the Portal Engine model, which the majority of people use now, you have to check the Widget that you are using, basically it boils down to a regular search or Smart Search.
If your using the ASPX Template model you may have to open up your source for the page and see which usercontrol file your using from ~/CMSWebParts/Search/ or ~/CMSWebParts/SmartSearch/
Once you figure out which user control you are using it s a matter of inspecting the Transformation that it uses. Most likely you ll be using one of the following:
CMS.Root.SearchResults
CMS.Root.SmartSearchResults
CMS.Root.SmartSearchResultsWithImages
Click on Edit Transformation and check out which field is inside the Call to SearchHighlight, normally, "Content". Then you know it s pulling from the main content of the document. I ve also seen this be tied to a different field like "Title" or "Caption". But the default is "Content".
If you still dont see results with part of the text, make sure you have a Smart Search Index setup, found in CMSSiteManager -> Administation -> Smart Search. If you don t see your site in the Index list then you need to add one. Make sure you rebuild it and optimize it (click edit on the row to get to those options). After that is all rebuilt then you should see the text appear under the result.