Write g(x) = 4x2 + 88x in vertex form.

from thales, who is often considered the first western philosopher, to the stoics and skeptics, ancient greek philosophy opened the doors to a particular way of thinking that provided the roots for the western intellectual tradition. here, there is often an explicit preference for the life of reason and rational thought. we find proto-scientific explanations of the natural world in the milesian thinkers, and we hear democritus posit atoms—indivisible and invisible units—as the basic stuff of all matter. with socrates comes a sustained inquiry into ethical matters—an orientation towards human living and the best life for human beings. with plato comes one of the most creative and flexible ways of doing philosophy, which some have since attempted to imitate by writing philosophical dialogues covering topics still of interest today in ethics, political thought, metaphysics, and epistemology. plato’s student, aristotle, was one of the most prolific of ancient authors. he wrote treatises on each of these topics, as well as on the investigation of the natural world, including the composition of animals. the hellenists—epicurus, the cynics, the stoics, and the skeptics—developed schools or movements devoted to distinct philosophical lifestyles, each with reason at its foundation.

with this preference for reason came a critique of traditional ways of living, believing, and thinking, which sometimes caused political trouble for the philosophers themselves. xenophanes directly challenged the traditional anthropomorphic depiction of the gods, and socrates was put to death for allegedly inventing new gods and not believing in the gods mandated by the city of athens. after the fall of alexander the great, and because of aristotle’s ties with alexander and his court, aristotle escaped the same fate as socrates by fleeing athens. epicurus, like xenophanes, claimed that the mass of people is impious, since the people conceive of the gods as little more than superhumans, even though human characteristics cannot appropriately be ascribed to the gods. in short, not only did ancient greek philosophy pave the way for the western intellectual tradition, including modern science, but it also shook cultural foundations in its own time.

i think you may have asked this twice, but i answered one of the

use wikipedia, i think they have this.

male citizens in athens could vote on all the decisions that affected the city and serve on juries. however, democracy was not open to everyone. citizen women and children were not allowed to vote. slaves and foreigners living in athens (known as metics) were banned from participating in government.