# Week 9

This week we worked on converting from standard for to vertex form by completing the square.

Ex: y=x²+4x-5

y= (x²+4x+4)-5-4

y=(x+2)²-9

# Week 8

This week, we focused on analyzing quadratic functions and changing them to parabola’s.

Identifying the y intercept of the graph of a quadratic function.

y= 3-14x+5x²

y= 3-14(0)+5(0)²

y=3-0+0

y=3

The discriminant is a number that shows if the value of x is rational/irrational/how many roots it has.

The formula we use to find the discriminant of a quadratic equation is b²-4ac

ex: 2x²-10x+3=0

The first step is to identify the values of a,b and c:

a=2

b=-10

c=3

We will then plug these numbers into the formula:

-10²-4(2)(3)

100-24

=76

The discriminant for 2x²-10x+3=0 is 76. This means that this quadratic equation has 2 irrational roots. This is because the equation is positive yet not a perfect square.

# Week 5- Factoring polynomials

This week, we spent reviewing factoring polynomials.

ex: x²+12x+20

Notice that this equation is rational. This means that we can easily factor this equation. To factor this equation, we want to look at which 2 numbers multiply into 20 AND add into 12. If we look at the numbers 10 and 2, we see that if you multiply them, they equal 20 and when you add them, they equal 12. This means that these 2 numbers will be used to factor. (x+10) (x+2) is the answer once factored. Once expanded, the product will be x²+12x+20. This means is a good way to make sure the factoring was done properly.

# Week 4- Multiplying and Dividing Radicals

Ex: $\sqrt{3}$ x $2\sqrt{4}$

$2\sqrt{12}$

As shown above, you multiply like normal when multiplying radicals. The radicand is multiplied with the other radicand and the coefficient is multiplied with the other coefficient.

This week, we started working with radicals. This week, I wanted to show how one would simplify radicals. I feel like this will help myself when studying for the final.

Ex. $\sqrt{27}$

when simplifying radicals, you want to look at the number you are using, in this case, 27, and finding what perfect square goes into it. For 27, it is 9 because 9×3=27.

We can square the 9 and but it outside the root and keep the other 3 on the inside because it cannot be squared. The simplified version of $\sqrt{27}$  is $3\sqrt{3}$

# Week 2- Geometric Series

This week, we started by learning how to find a common ratio for geometric series’. Geometric series are when one number is multiplied by the same number each time.

Ex. 3, 9, 27

To find the common ratio (r.) We have to divide the first term by the second term. $\frac{9}{3}$ = 3

`This means that the common ratio is now 3. When we multiply each term by 3, the geometric series continues correctly.

# Week 1- Arithmetic Sequences

This week, we worked with arithmetic sequences.

2,4,6,8,10…

Each of the numbers above are considered terms. The number 2 is considered $t_1$

Part 1:

When finding a term, we use the formula: $t_n$ = $t_1$ + (n-1)d  (d represents difference between terms.)

For finding term 50, we will use this formula.

$t_{50}$ = 2 + (50-1)2

$t_{50}$ = 2 + 98

$t_{50}$ = 100

Part 2:

When finding the sum of all terms, we use the formula: $s_{50}$ = $\frac {n}{2}$ + ( $t_1$ + $t_n$ )

I will be using the same sequence from above to find the sum.

$s_{50}$$\frac {50}{2}$ + ( 2 + 50)

$s_{50}$ = 25+ 52

$s_{50}$ = 77

# Persuasive Essay Corrections

The Power of Leading With Love

Who is a more effective leader? One that leads with love or one that leads with fear? In the novel Lord of the Flies by William Golding, a group of young school boys survive a plane crash but face the struggle of survival. As the boys stray away from civilization they are faced with many conflicts. Two boys, Ralph and Jack, emerge as the main leaders. They both have different views on how the island should be organized. Ralph is civil and Jack is savage. Ralph is a more effective leader because he leads with love. Based on the many conflicts and unfortunate events the boys face, Ralph handles the them with insight and maturity.

When it comes to how the island is run, Ralph does everything in his power to preserve all forms of civilization. Initially, when the boys first crash onto the island, he finds a conch shell and blows into it, assembling a meeting. As the story line progresses, the conch is used as a device symbolizing freedom of speech and civilization. Whoever held the conch had the right to speak in these meetings. In any case, this helps the boys keep order on the island. Ralph strongly believed in enforcing rules: “We ought to have more rules. Where the conch is, that’s a meeting” (pg.42.) In a civil world, there are rules and punishments. According to Golding’s beliefs, all humans are born evil; the only thing stopping them from committing evil acts is law and consequences. Ultimately, in order to create a civil island, Ralph also believes they needed order. Ralph try’s to go back to civilization by maintaining the fire in an effort to get passing ships to notice and save them. In Ralph’s opinion “The fire is the most important thing on the island. How can we ever be rescued except by luck, if we don’t keep the fire going” (pg.31.) This shows that his priority is to get off the island; he can see that the boys like to play because they are having fun without adults but reasonably, they can’t stay there forever.

Contrary to how Jack only focuses on hunting, Ralph always looks at everyone’s needs and finds ways to support them. Even through his frustration from the lack of help he receives from his peers, his love for them shines through as he always does the tough jobs: “I work all day with nothing but Simon and you come back and don’t even notice the huts” (pg.55.) Generally, Ralph’s actions go unnoticed but that doesn’t stop him from making huge contributions to the needs of the boys. Ralph does his best to organize the boys into groups in order to efficiently complete needed tasks: “‘I’m chief,’ says Ralph, ‘because you chose me. And we were going to keep the fire going. Now you run after food’” (pg.137.) Without Ralph, the boys would only focus on having fun and not on survival; Jack is only focused on playing and killing whereas Ralph focuses on everything.

Furthermore, Ralph views communication as a necessary aspect needed on the island for their survival. Ralph continues to enforce how important communication is in order to be civilized. The conch was the most sufficient form of communication. It enables them to come together for meetings. As Ralph explains, “He can hold it when he’s speaking and won’t be interrupted” (pg.33.) This is a system Ralph came up with. The conch represents the power of speech and civilization. Ralph thought of this idea so everyone can have their ideas be heard. Ralph also has the idea to have one leader on the island. Essentially, this is important because without a leader, there would be a huge conflict of ideas. After talking to the boys, Ralph decided that “Seems to me we ought to have a chief to decide things” (pg.12.) The idea of having a leader and using the conch shell shows how Ralph searches for order in everything.

Despite all of Ralph’s positive qualities, some may argue that Jack is a more effective leader because more people choose to follow him. Jack uses fear to rule the boys. He leads the boys through manipulation. The boy’s fear the beast and Jack fantasizes it which warps their perception of reality. He also tortures Sam and Eric and forces them to join his tribe. There were so many areas of needs on the island; Ralph realizes that without shelter and food, there would be no chance of survival whereas Jack creates another problem from his figment of imagination and pleasure of killing.

Without a doubt, Ralph is a more effective leader because he leads with love and he looks after all areas of need. He takes action on what the boys need in order to survive and has the most mature point of view out of anyone on the island. He implements his plans and takes action on making a positive difference on the island. He is the only level-headed leader who thinks about using a fire to be rescued, building huts that will protect them from storms and finding a reliable source of food; these are all aspects of life that are important for the boys survival.

Works Cited

Golding, William. Lord of the Flies. New York: Coward-McCann, 1962. Print.

# Name Controversy Corrections

Name Controversy

Team names targeting Native American stereotypes should not be changed. Although there is a lot of controversy surrounding the names and logo’s of certain sports teams, according to a Washington Post poll, only 23% of native Americans wanted controversial sports teams names aimed at them to be changed. In a lot of cases, non native American people are speaking on behalf of native Americans on what they believe is respectful instead of actually listening to them and their ideas. In fact, the Washington Redskins name and logo was once created by someone of native American descent. It was not created to bash and harm First Nations people; contrary to popular belief, it was meant to do the opposite: show pride and resilience. “I’m proud of being Native American and of the Redskins,” said Barbara Bruce, a Chippewa teacher. People tend to interpret ideas in the wrong way. The only way to respect the Native American people is to listen to them. If they say they are fine with the name, there is no reason it should be changed. If it doesn’t affect First Nations people, why should it affect everyone else? An example is when NBC sportscaster, Bob Costas, claimed the Redskins name is “an insult, a slur, no matter how benign the present-day intent.” Whereas in the video produced by “Redskins Facts” on Youtube titled “Redskins Reservations Interview,” none of the people on that certain first nations reserve seemed bothered by that name. Overall, the name should not be changed. It is part of their history and branding and, it is not negatively impacting first nations as much as many people believe.

Sources: