Endocytosis is a form of active transport hence require enegry powered by ATP. The amoeba needs to change shape and engulf and envaginate the particle and then use vessicle transportation to get the materials into the cell. This requires that the cytoskeleton - composed of tubules and filaments - contracts and relax accordingly. This requires energy by ATPs just like the myosin and actin of muscle.
Phagocytosis, another form of endocytosis, is used by some cells such as immune cells to engulf foreign material and then destroy them by use of lysozymes. This is how phagocytes protect the body from invaders.
