The derivation for the equation of a parabola with a vertex at the origin is started below.

=
(x)2 + (y – p)2 = (0)2 + (y + p)2
x2 + y2 – 2py + p2 = y2 + 2py + p2
If the equation is further simplified, which equation for a parabola does it become?
x2 = 4py
x2 = 2y2 + 2p2
y2 = 4px
y2 = 4py

Read the following passage "you're not here to read books, you're here to learn! " the childwrangler's voice screeched as we kept our picks moving rhythmically against the school walls. we had all heard about a time, back in the dark ages, when children read books at school. they say school was even a building above ground. but that was obviously dangerous. how could society thrive if all the children sat around reading all day? when would they have time to learn about veins of coal, processing fuel, and all that stuff? school was important.what two central ideas in this story are most closely related? a. the importance of literature and the dangers of miningb. humankind's basic survival needs and independence c. the nature of learning and societal dysfunctiond. the powers of rumors and abuse of authority

How does the author's purpose affect his or her text structure

(1) fire extended humans’ geographical boundaries by allowing them to travel into regions that were previously too cold to explore. (2) it also kept predators away, allowing early humans to sleep securely. (3) fire, in fact, has been a significant factor in human development and progress in many ways. (4) other obvious benefits of fire are its uses in cooking and in hunting. (5) probably even more important, however, is that learning to control fire allowed people to change the very rhythm of their lives. (6) before fire, the human daily cycle coincided with the rising and setting of the sun. (7) with fire, though, humans gained time to think and talk about the day’s events and to prepare strategies for coping with tomorrow. the sentence that expresses the main idea is: (type the number of the sentence. then click “go.”)