Final answer:
The vital centers for control of heart rate, respiration, and blood pressure are located in the medulla oblongata of the brainstem.
Step-by-step explanation:
The vital centers for the control of heart rate, respiration, and blood pressure are located in the medulla oblongata. This portion of the brainstem is responsible for the regulation of these vital functions. The medulla contains a collection of nuclei known as the cardiovascular center, which manages the autonomic control of the heart and blood vessels. When blood pressure fluctuates or changes in blood concentrations of oxygen, carbon dioxide, and hydrogen ions occur, these centers adjust the function of the cardiovascular system to maintain homeostasis. Additionally, input from the hypothalamus can influence the medulla to modulate cardiovascular system activity due to factors like stress or anxiety. Autonomic fibers such as the cardiac accelerator and vasomotor nerves alter heart rate and blood vessel constriction accordingly.