I apologize in advance for my lack of knowledge. I don't know a great deal about working with this program, so I'm learning as I go. I am wanting to take the free Landsat data that I have downloaded and turn it into a NDVI shapefile for use in another agriculture program. 

I have downloaded the data and imported Bands 4 and 5 into QGIS. Since this is for a particular field, I used a shapefile of the field boundary to clip the image.  I then used the Raster Calculator to generate a GeoTIFF using the expression (Band5-Band4)/(Band5+Band4).  I also changed the layer properties so that I can visualize the data on a RedYellowGreen scale. This looks good so far.

I now need to turn this clipped GeoTIFF into a shapefile so that I can import it into my other program.  I have tried the polygonize (Raster to Vector) but this doesn't seem to give me what I am needing.  Could someone point me in the right direction, please?