Is a bush in your back yard is it alive according to the characteristics of life

To me if grows then its alive

Yes it is. 
1. it has a definite structure and organization -- organic (carbon-based molecules) 
2. it metabolizes -- its leaves are green and the green color is due to chlorophyll which is vital in photosynthesis. 
3. it maintains internal environment/homeostasis -- it does not dry up which means it keeps the water level inside at a constant level. 
4. it can reproduce -- that's why it is not extinct or endangered 
5. it grows -- that's why i give it a trim every few weeks 
6. i don't see my bush react to stimuli, but plants generally grow towards an area with more sunlight if it is not always exposed to sunlight. 
7. my bush has thorns as an adaption (which is a product of evolution) to defend itself

Nucleus is the organelle that contains chromosomes

Reproduction i think