If it has bright red flowers and is a shrub, it's probably a "japonica" (flowering quince). Scientific name Chaenomeles. It's very popular, and very easy to grow. I never tried cuttings of it, but I suspect they wouldn't be too hard.

Aha! Thanks so much, 'Dirt! It is Japonica. Lovely what you can find out when you google the correc thing. I'm gonna try it! ~~Michelle

It's one of my favorite shrubs. And, depending on which one you buy, you MAY get edible fruit in the fall!

Can you root it by cuttings?

I've never tried it, but here's what I found on one page:

" Propagation

Chaenomeles species can easily be generatively propagated. Germination rates between 95% and 100% are frequently obtained, provided that seeds are not allowed to dry out before being properly stratified. A month at 2ð to 4ðC in moist substrate is sufficient (Tiits 1989) but in commercial propagation a period of 2�"3 months or longer is commonly used. Cultivars must be vegetatively propagated. Whereas chaenomeles cultivars can be grafted, as well as propagated by root pieces, by layering or by hardwood cuttings, softwood cuttings are preferred for commercial scale enterprises. There is, however, much variation in rooting ability among genotypes (Wells 1955; Eley 1970; Kviklys and Rumpunen 1996). Rooting percentage can be strongly increased by use of growth regulators (typically 30 ppm IBA for 18 h, or a quick dip in 1000 ppm IBA) but size of the cutting is also important. Large cuttings (above 20 cm) root rapidly, produce more roots, and show better winter survival (Wells 1955; Kviklys 1998). Etiolation of shoots may retard rooting (Blain and Dixon 1984) and should therefore be avoided. Protocols for micropropagation have also been successfully developed (Panavas 1994; Stanys 1996, unpubl. data). Due to high costs, micropropagation may be limited to production of stock material for later propagation of cuttings."

http://www.hort.purdue.edu/newcrop/ncnu02/v5-385.html

So take a big softwood cutting, dip it in rooting hormone, and treat it like any other cuttings. Good luck!

or air layer them. Air layering is even easier and more reliable than softwood cuttings, but may take a little longer.