Lanceolate dentate pennate shaped leaf, similar to rose bushes, aquifolium, Japonica, and media charity bushes or shrubs.

It feels like a rose bush on the twig, but the leaves are more pointy and thick. Does this help? Can you tell me what varieties have these same leaf shapes?

Scarletdaisies - you are obviously really getting into plants but I think you are setting a bit too much store by keys and books etc. I'm afraid the plant in the picture is not a rose in a million years. And the other names you give are not actually species names but should all be preceded by 'Mahonia' e.g. Mahonia aquifolium. I don't know what your plant is but it is definitely neither Rosa nor Mahonia.

I know it's not a rose, I have a few wild rose bushes in my yard I pay no attention to. I found a plant leaf guide, since no one attempted to name mine, I thought I would help describe it, so anyone who at least read of a plant similar, they would mention it.

It is also similar to a European Ash tree, but I know it's some kind of weed, but the only leaf I could find similar is the ones I mentioned above.

That is very useful to know, I'm leaving these links, so if anyone wants to research on the internet what they have, they will have a way to describe it. I found some good pictures near what I have by the description alone in a search.

http://www.botanical-online.com/hojastiposangles.htm

http://en.wikipedia.org/wiki/File:Leaf_morphology.svg

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Just humor me, I'm not trying to get scientific! LOL! I'm just curious why two of these plants perfectly spaced popped up where nothing but marigolds were planted. It's the prettiest weed I've ever seen. I can vouch for this, for the past two years, I've never seen any weed in this garden that looked like this especially where it's growing.

What made me think of a rose is the strength of the thin twigs on it, plus since I borrowed leaves from my dad's yard, there is rose of Sharon bush growing in it, and maybe the seeds took and grew.

It may be a rogue off-type Marigold which sometimes appear in hybrid strains.

Here is a link that might be useful: Let's Talk About Hybrids and Standards

Thank you, I think you're right.

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This one above I found in a search, so it has to be. Some I planted from a package, some from some small ones I collected seed from.

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Even with all those big words, marigolds never came up in an internet search, go figure.