College Algebra, Chapter 4, 4.1, Section 4.1, Problem 28

A quadratic function $f(x) = 1 - 6x - x^2$.

a.) Find the quadratic function in standard form.


$
\begin{equation}
\begin{aligned}

f(x) =& 1 - 6x - x^2
&&
\\
\\
f(x) =& -1(x^2 + 6x) + 1
&& \text{Factor out -1 from the $x$-term}
\\
\\
f(x) =& -1 (x^2 + 6x + 9) + 1 - (-1)(9)
&& \text{Complete the square: add $9$ inside the parentheses, subtract $(-1)(9)$ outside}
\\
\\
f(x) =& - (x + 3)^2 + 10
&& \text{Factor and simplify}

\end{aligned}
\end{equation}
$


The standard form is $f(x) = - (x + 3)^2 + 10$.

b.) Draw its graph.







c.) Find its maximum or minimum value.

Based from the graph, since the graph opens downward the maximum value of $f$ is $f(-3) = 10$.

Why is Matt upset with Celia at the beginning of the story?

Matt is upset with Celia because yet again, she is leaving for work and he’ll be left locked up alone in the house all day. Matt is curious about the world outside that he has only interacted with by way of peering through the window. Celia would never allow him outside because it is unsafe for him. Matt does not know that he is a clone, purposefully lab-manufactured to provide El Patron with a replacement heart in the future. However, humans, and more so, those in El Patron’s household, loathe clones and often go out of their way to harm them. For this reason, Matt is put under the safe custody of Celia, a cook in El Patron’s house.
He is finally discovered from his safe hideout and momentarily endangered in the hands of El Patron’s people. El Patron saves Matt and accords him a respectable life, including an exclusive bodyguard. Matt finally escapes his fate as El Patron’s heart donor and moves to Aztlan.

How did tobacco save Jamestown's colony?

Jamestown, an English colony, was founded in 1607, but by 1614, disease, famine, and war with the Native Americans turned the establishment into a place of suffering. The colony seemed lost until John Rolfe, the man who married Pocahontas, decided to cultivate tobacco in the region. Rolfe chose to grow Nicotiana Tabacum, a strain of tobacco that was being grown in South America by the Spanish. 
Rolfe was successful. Colonists took the first shipment of tobacco to London in 1614 and it was quickly sold. The crop was so successful that Rolfe sailed over to London to discuss its success with King James I who agreed to allow Jamestown to continue growing and selling tobacco. King James I did not support the use of tobacco, but he saw that it would be the only way to save his precious colony. Not to mention, he realized that England could make a fortune off the import and sales taxes from the crop. Tobacco was so successful that the colony had produced and sold over 750 tons of it by 1639, just twenty-two years later. Tobacco turned Jamestown into a bona fide settlement and the first permanent English colony in the Americas.

The Jamestown colony was first and foremost a mercantile enterprise. The stated aims of the company were to find and develop the region’s natural resources—gold, silver, and precious gems especially. Failing to find precious metals and gems, the company turned to trade as a way to grow the colony. In the early years, many colonists viewed Virginia as a place to make a quick fortune and intended to return to England as soon as possible. Few early adventurers sought to establish deep roots in the colony.
First brought to Europe by Columbus, tobacco was a known commodity to English merchants. Spain's monopoly on new world trade however created a trade deficit for England, which the Virginia Company was intended to abate. The tobacco plant native to Virginia, Nicotiana rustica, was shared with the English colonists by the native Powhatans during the time of the ill-fated Roanoke colony. The Virginia plant species was bitter in flavor compared to the milder tobacco grown in the Spanish colonies of the Caribbean.
In 1612, John Rolfe experimented with seeds of the Caribbean species, Nicotiana tabacum, which did well in the fertile Virginia soils. In 1614-15, after just two years of cultivation, more than a ton of tobacco was exported to England. By 1630 that figure rose to a half million tons, which more than doubled by 1640.
As exports of the new English tobacco proved to be a valuable cash crop for the Virginia Company, it spurred migration to the colonies by eager fortune seekers. Jamestown, as the Virginia colony's entry point and principal center, and its surrounding outpost settlements, began to thrive as new colonists sought new land to cultivate. The company's offer of 50-acre land grants to new immigrants opened a flood of new migrants entering and spreading out from the James River valley.
The land-grant incentive gave claimants an additional 50 acres for any immigrants whose passage they paid. This program and the land requirements of tobacco cultivation, enabled farming in Virginia to escalate from small plots managed by a single farmer, to large, plantation-style farms requiring a larger workforce to maintain. This opened the gates to the system of indentured servants, who came as bonded laborers, and then the import of African slaves in 1619.
Between 1618 and 1620, the English population of Virginia grew from a few hundred to nearly 1,500 people. Through the first decade of settlement, the population was almost exclusively young, unmarried men. In 1620 the first single women began to arrive in the colony. The tide of immigration changed due to the tobacco boom of the 1620s as families now arrived seeking to live as permanent settlers. 

IN THE FEDERALIST 10 1. Identify the part of the national government that was originally most closely tied to citizens and explain how it was tied to citizens. Explain two ways The united States Constitution limited majority rule. Please help this parent who made her child do the wrong summer homework.

Considered among the most important documents in United States history, Federalist #10, written by James Madison under a pseudonym, provides one of the Founding Fathers' most eloquent arguments in support of the Constitution. That this particular document constitutes a warning to the public against the factionalism into which Madison and others feared a pure democracy would descend makes it especially noteworthy. Many Americans understand that the system of government established in the Constitution is not a pure democracy but rather a republic. In other words, the public elects individuals to go to Washington, D.C. to represent its interests. If every voting-age citizen voted on legislation, the process by which laws are made and treaties ratified would have been too unwieldy and too riven by factions of like-minded individuals whose interests may ignore those of the larger good; in other words, factional interests would overshadow the interests of the nation as a whole. As Madison wrote in Federalist #10:

"No man is allowed to be a judge in his own cause, because his interest would certainly bias his judgment, and, not improbably, corrupt his integrity. With equal, nay with greater reason, a body of men are unfit to be both judges and parties at the same time; yet what are many of the most important acts of legislation, but so many judicial determinations, not indeed concerning the rights of single persons, but concerning the rights of large bodies of citizens?"

There is a reason that the first article in the Constitution of the United States establishes the legislative branch of government: the Founders believed fervently that the representatives of the public (mainly, the members of the House of Representatives) would be best suited to ensure that the public's voice was always heard. Popular representation, however, was not an end in itself; the need to protect against complete domination of the majority over the minority was also a priority. Minority views had to be represented and respected. Once again quoting Madison:

"The apportionment of taxes on the various descriptions of property is an act which seems to require the most exact impartiality; yet there is, perhaps, no legislative act in which greater opportunity and temptation are given to a predominant party to trample on the rules of justice. Every shilling with which they overburden the inferior number, is a shilling saved to their own pockets."

The House of Representatives, despite its closeness to the public it represents, is ruled by the majority party. The minority party in the House of Representatives enjoys almost no power except when individual members of the minority party succeed in establishing alliances on certain issues with members of the majority party, which happens regularly on parochial matters important to individual states or districts. This is why the Constitution's authors established the Senate. It is in the United States Senate that the rights of the minority are protected. Individual members of the Senate enjoy considerable power relative to their number. Individual senators can block legislation from being debated and voted upon by the Senate, and individual senators can block presidential appointments from being confirmed for the positions for which they were nominated. Whereas the minority in the House of Representatives enjoys minimal power, the minority in the Senate enjoys power out of proportion to its percentage of the whole. 
This, then, is how the Founding Fathers ensured that majority rule did not descend into dictatorship. The Constitution established a legislative branch of government before any other branch (namely, the executive and the judicial) and also established a "higher" body within the legislature, the Senate, in which minority rights would be protected. 
Minority rights were also protected in the Constitution through the establishment of the executive branch of government. The chief executive, or president, enjoys a great deal of power, but his or her power is checked by that of the other two branches of government. Presidents, though, might represent the minority party in Congress, which happens from time to time when the public elects a divided government (the president's political party is different from that which enjoys the majority in one or both chambers of Congress). The president's power to veto legislation, which can only be overridden by a two-thirds vote by both chambers (Article I, Section 7), serves as an important check on the legislature.

In detail please explain the relationship between media literacy, populism, and civic action.

To effectively identify and discuss the relationship between the three terms, one needs to define them first. 
Media Literacy:
The Center for Media Literacy (CML) defines the term as "the ability to access, analyze, evaluate and create media in a variety of forms." An additional definition states that Media Literacy "...provides a framework to access, analyze, evaluate, create and participate with messages in a variety of forms — from print to video to the Internet. Media literacy builds an understanding of the role of media in society as well as essential skills of inquiry and self-expression necessary for citizens of a democracy." 
The National Association for Media Literacy Education (NAMLE) defines Media Literacy as "...the ability to access, analyze, evaluate, create, and act using all forms of communication... Media literacy represents a necessary, inevitable, and realistic response to the complex, ever-changing electronic environment and communication cornucopia that surround us."
In its most basic form, therefore, Media Literacy refers to one's ability to understand, use, and act on all forms of communication.  
Populism:
The Cambridge Advanced Learner's Dictionary and Thesaurus provides a straightforward and direct definition of the term and defines populism as "Political ideas and activities that are intended to get the support of ordinary people and give them what they want."
The Business Dictionary provides a relatively detailed definition:

In general, ideology or political movement that mobilizes the population (often, but not always, the lower classes) against an institution or government, usually in the defense of the underdog or the wronged. Whether of left, right, or middle political persuasion, it seeks to unite the uncorrupt and the unsophisticated (the 'little man') against the corrupt dominant elites (usually the orthodox politicians) and their camp followers (usually the rich and the intellectuals). It is guided by the belief that political and social goals are best achieved by the direct actions of the masses. Although it comes into being where mainstream political institutions fail to deliver, there is no identifiable economic or social set of conditions that give rise to it, and it is not confined to any particular social class.

Populism, in general terms, refers to the appeal made to ordinary citizens by promising to give them what they want to gain their support. 
Civic Action
The Spencer Foundation says the following about civic action:

...include(s) any public action that addresses social issues or power relations—protesting, boycotting, or blogging as well as voting and lobbying legislators. 

According to Giovanni Moro, civic action "can be defined as a form of citizenship practice consisting in mainly collective initiatives aimed at implementing rights, taking care of common goods or empowering citizens. It can be addressed both to governmental or private interlocutors as well as to the general public. It implies the exercise of powers and the use of specific tools on the citizens’ side."
In our modern world, saturated by the media, it becomes apparent how a link between these three concepts can exist. We have witnessed how effectively the media has been utilized in the past decade, for example, not only to influence thinking and win support but also to encourage action and bring about real change. In practically all of these instances, appeals were made to common people: your "regular guy" and "the man in the street." These are citizens who would likely be disgruntled by a particular state of affairs because they feel that they are either neglected, discriminated against, or being treated unfairly. They would desperately desire change. 
These campaigns were successful because all those who lead them used people's relationship with and understanding of the media as devices to appeal to the general public and encourage civic action, sometimes with not too positive and, at times, even disastrous consequences. A good example is the "Leave" and "Remain" campaigns in the UK. Politicians on both sides appealed to the general public's fears, and the Leave campaign, especially, won the vote by using a populist platform. The media was used extensively to illustrate the current situation and contrast it with what was presented as a better alternative. It goes without saying that in such cases the general public is told what campaign leaders assume they want to hear—regardless of whether the information provided is accurate and true or not.
The electoral campaign in the US is another example of how the relationship between media literacy, populism, and civic action was used to win votes. The often-stated belief is that Donald Trump won the election because of social media. The public at large is constantly exposed to and bombarded by the media. The vast number of media platforms make it practically impossible to ignore the constant stream of information that they provide. The Trump campaign focused on using a populist platform and announced its agenda through the media. This hugely successful crusade exploited the fears of the public at large, and their anxiety was expressed in the form of votes in favor of Trump's candidacy.  
It should be patently clear that the public's current relationship with the media has made it easier to appeal to the common man and drive him to take action.

Who is Sisyphus? Why is he rolling a rock up the side of a mountain?

Sisyphus is a character in Greek mythology who is condemned to spend his life rolling a boulder up a mountainside. There are some variations on the Myth of Sisyphus, but it is generally told that he was the king of Corinth. He was exceptionally clever, in some versions described as a highwayman, and is even said to have cheated Death! For being so bold, the Gods set a punishment for Sisyphus that he could never overcome. He must roll a heavy boulder up a mountainside, only to have it roll back down once reaching the top. He must perform this task over and over for all eternity. 
Sometimes people will call a repetitive and futile action a "Sisyphean task," referencing the Greek myth.
https://www.britannica.com/topic/Sisyphus

https://www.nyu.edu/classes/keefer/hell/camus.html

What scene throughout the novel The Boy in the Striped Pajamas would be described as being foreboding?

Foreboding is the feeling that something bad will eventually happen. One example of a foreboding scene throughout the novel takes place in Chapter 19 after Bruno has dressed up as a Jew and crawled underneath the fence of the concentration camp. When Bruno walks through the concentration camp, he mentions to Shmuel that he doesn't like it in here. All of a sudden, ten Nazi soldiers surround the area in which Bruno and Shmuel are standing and give them a command to march. A crowd of prisoners gathers and begins to march. Bruno and Shmuel are trapped in the center of the group and collectively move with the other prisoners. As they are marching, Bruno looks up in the sky and notices that clouds are becoming darker. There is also the sound of loud thunder overhead and rains begins to pour down heavily. The weather can be described as being foreboding during this scene. The reader can assume that something terrible is going to happen based on the precarious situation Bruno and Shmuel are in, as well as the ominous stormy weather. The group of prisoners is lead to a gas chamber where Bruno and Shmuel die while they are holding hands.