A couple of years ago I got into a discussion in an online forum about the wisdom of using a tele-extender on a zoom lens. I was surprised to see a number of people steadfastly maintaining that one could not achieve professional quality results with a tele-extender on a zoom. Just wouldn't work, period, they said.

My own experience contradicts that viewpoint. I've used a Canon EF 1.4X II extender on my 70-200mm F/4L IS USM zoom since 2005, and I've been pleased with the results. I like the combination because it is light, long, compact, affordable, and hand-holdable. Mounted on an APS-C camera like my Canon 60D with a 1.6X 'crop factor', the 35mm equivalent maximum focal length is 448mm with a maximum aperature of f/5.6.

Below is a photo of a 12 spot dragonfly taken with this combo. The upper frame is the final cropped edit. The middle frame shows a 100% crop of one wing so that you can get an idea of the sharpness achieved. The bottom frame is a screenshot showing what I cropped away.

However, I would add that good mechanics are essential.  Either use a sturdy tripod or a high shutter speed, and check your focus carefully.  Use the sharpest f/stop available, usually f/5.6 or f/8.