This week in precalc, I learned how to tell if quadratic equations are real, equal, unreal, or unequal, using their graph.
For a graph to be real and unequal, it must have two x intercepts on a graph, giving it two real solutions.
For it to be real and equal, it must have one x intercept, giving it a single solution.
If it’s unreal and unequal, it will have no x intercept, giving it no real solutions.
This week in Precalc 11 I learned the quadratic formula and its use. The formula is an easy way to solve most quadratic equations, and it looks like this:
This formula can be input with the pieces of a quadratic formula if with the numbers being
This formula can take a while to use in terms of calculations and inputting information, but its much more straightforward than factoring or completing the square. Additionally, it’s a great go-to if a calculator is at hand.
In Lord of the Flies, many of the characters commit all kinds of nasty and horrific acts, but of all the despicable children on that god forsaken island, Jack Merridew is the worst of the worst. With all of his actions, decisions, and behaviours, he has made it clear he wants to be known as the Worlds’ Biggest Tool. And I am here to provide the evidence that will ensure he earns that title.
Throughout the book, Jack continually morphs into a vile, savage, little child. Right at the beginning of the book, he shows signs of being a bully and treating others like trash. It’s fairly obvious the choir kids don’t enjoy being under Jack’s thumb. As events progress, Jack continues to undermine, bully, and scare various children and characters in order to keep them in check, and this just further displays how much of a jerk he is.
For starters, he treats Piggy like absolute garbage. He physically bullies him, when he pushes and hits Piggy and breaks his glasses, and constantly verbally harasses him, with instances such as: “You’re talking too much,” said Jack Merridew. “Shut up, Fatty.”
“You’re no good on a job like this.” “All the same –” “We don’t want you,” said Jack, flatly. “Three’s enough.”
“Jack pointed suddenly. “His specs–use them as burning glasses!” Piggy was surrounded before he could back away. “Here–let me go!” His voice rose to a shriek of terror as Jack snatched the glasses off his face.”
“This from Piggy, and the wails of agreement from some of the hunters, drove Jack to violence. The bolting look came into his blue eyes. He took a step, and able at last to hit someone, stuck his fist into Piggy’s stomach. Piggy sat down with a grunt. Jack stood over him. His voice was vicious with humiliation.“You would, would you? Fatty!” Ralph made a step forward and Jack smacked Piggy’s head. Piggy’s glasses flew off and tinkled on the rocks.”
All of these are sound evidence of times Jack has been a bully to Piggy, and while Piggy is his biggest victim, he’s not his only one. Another great example was Robert’s treatment, or how Jack had already asserted dominance over the boys’ choir.
“The circle moved in and round. Robert squealed in mock terror, then in real pain. “Ow! Stop it! You’re hurting!”
It’s plain to see that Jack will find all kinds of opportunity to bully, mock, or hurt others, and takes great joy in it. One factor in his overall extreme jerkiness.
As soon as we meet Jack, one thing is for certain: he wants power. He wants to lead. There are few twelve year-old choir boys as power hungry as Jack, and it shows, as he already has extreme dominance over the other boys in the choir. As time goes on, Jack continually tries to find power or leadership through manipulating people into being drawn to him, or simply defying the law of Ralph, who is above him in the hierarchy. Yet, despite Jack’s insatiable need to lead and control, the guy can’t do any of that.
Jack is entirely, completely barren of any sort of proper leadership skills. He cannot take care of his people, make smart decisions for them, or control his own impulses. All he wants to do is follow his primal, natural instinct, which in the case of his leadership on the island is to hunt.
Jack seems to stop at nothing to try and get at a leadership role on the island, from threatening and harming others to intentionally throwing a wrench into Ralph’s plans to manipulating others. He uses all kinds of methods, some rather reckless and consequential, simply because he wants to be in charge.
Clearly, Jack is an irresponsible person who wants to put himself in charge at any cost despite having no skill in leadership. His methods cause problems, his goals cause harm, and his overall values in terms of leading are quite idiotic. Very obviously the sign of a giant tool.
I think we can all agree that murder is wrong. And if you don’t agree with that, then you may very well be Jack Merridew. In Lord of the Flies, Jack is indirectly responsible for the deaths of multiple children on the island: Piggy, Simon, and the birthmark kid. Not only is it wrong to begin with to kill someone or be at fault at all, but without his influence, the others may have kept their lives. He was also supposed to be one of their superiors, there to protect him, though he does the exact opposite.
To start, Jack Merridew brews and develops the tribe of savage hunters into what they are. They’re bloodthirsty, feral, and wild due to his teachings and leadership of strength and fear. Because of this, they so easily and quickly resort to killing to solve their problems, as evidenced with Roger easily dropping a boulder on Piggy and the boys all killing Simon in their frenzy of tribal rituals.
Not only that, but Jack was largely responsible for the maintaining and watch of the fire. However, he poorly organizes and enforces those tending to the flames, and thus it easily spreads into a large forest fire, believed to have killed the littl’un with the birthmark.
So, clearly Jack is irresponsible not only with his leadership, but others’ lives. He willingly allows and teaches others to be okay with murder and harming others.
Possibly the most vile of Jack’s crimes, Jack, with the help of his followers, hunt, attack, and kill multiple wild pigs on the island. Pigs are adorable, lovable, and not vicious at all, so it was hard enough to sit through Jack’s tribe killing pigs.
However, with the added fact that they tortured and sodomized a pig at one point, as well as brutally displayed its head, it becomes apparent that he truly is a monster. They did all that to a helpless mother pig, and they’re just okay with it, all under Jack’s command. I have no clue how anyone could condone such evil actions, and this is the last piece of evidence needed to prove Jack is a giant tool, an evil child, and a terrible human being (if you can call him that).
So, for those that somehow didn’t agree with me before this post, you can clearly see that Jack is nothing but a little ball of cruelty, and should have no sympathy or love whatsoever. He truly is the “Biggest Tool to Ever Walk the Earth”.
This week in Precalc I learned the acronym to help you when determining how to handle quadratic equations and trinomials: CDPEU (Can Divers Pee Easily Underwater). This acronym means Common Factors, Difference of Squares, Patterns, Easy, Ugly.
To start, you try and look for any common factors, which is pretty self-explanatory. If there are common factors, you’ll be able to reduce it right there before factoring.
Then, you see if there is a difference of squares, which also quite clear in what you need to do. If there is a difference of squares, you can factor it like so: a2 – b2 = (a + b)(a – b).
Next is patterns, which is telling you to look for a basic pattern such as a trinomial layout like: 
After that, see if it’s an easy question, where you can factor it easily with two numbers that multiply to the end term and add to the middle term.
Finally, check if it’s an “ugly” expression, meaning you’ll need to do some more work to solve that specific question, such as grouping or guess and check.
All in all, that’s the best way to identify and figure out how to solve various equations and expressions.
This week in math I learned when simplifying radicals, you must always have at least one of the simplified factors be a perfect root of whatever the index is. If you attempt to factor a number that has no perfect roots as factors, then you’ll be doing nothing helpful for yourself.
For example, if you are factoring the square root of 27, you will be able to do so as it has a factor of 9, which can be reduced to 3, allowing the radical to be simplified.
