The brachial artery supplies blood to the muscles on the upper arm and elbow joint, being the main vessel supplying this region. Therefore, it is located in the arm.
The femoral artery is the main vessel supplying blood for the legs. Therefore, it is located in the thigh.
The carotid artery carries blood and oxygen to the brain, being located in the neck.
The final answer is:
brachial - arm
femoral - thigh
carotid - neck