Week 14 – Graphing Reciprocals of Quadratic Functions

This week I learned how to graph quadratic reciprocal functions.

Here is a common question:

This question asked me to figure out the parent function of the graph. I knew it was c, because I drew the parent graph by going through the invariant points. I also knew that the graph only had one root, because there was only two hyperbolas. Then I used 1,3,5 to draw the rest of the graph.

Math Journal #2 and #3

1) Reflection for Qustion #7 pg 567

The question is: Consider the graph of the function with the equation y=2.

This is the lesson when we learned y=mx+b and the concept was pretty simple for me. Y= 2 means that the y-int equals 2 and that means that the line on a graph will be a horizontal line. In this question u had to state the values of m and b. Their so no slope so m=0 and I imputed the yint into b. Drawing the line on the graph was easy because it is just a straight line. I kind of got confused when they asked for the x int because on the graph the line does not go by x and then I realized that there is no x int. I remembered how to state the domain and range from the last unit. I learned from working on this question that using graph is a very good visual to help my learning.  I also learned to think outside the box. I think before the test I will need to study these types of questions and ask more questions about them. I will prepare myself by doing the practice test before the real test.

2) The x-intercept is where the function intercepts the x-axis. The y-intercept is where the function intercepts the y-axis.
When you look for the x-intercept given a equation, you set y = 0 then solve for x. Why is that?

You set y = 0 to find x because when y = 0 that means the line has to be going through x. When you solve for x you are isolating x and finding the x intercept, where the line is going through x on the graph. For example at the point (5,0) y = 0 and x = 5 and 5 is the x intercept.

Example: How do you find the x and y intercept for the equation :

y = \sqrt{x}-4 latex?

To find the x intercept you set y = 0 and solve for x. You plus 4 on both sides and then undo the sqrt by squaring the number. To find the y intercept you set x = 0 and solve for y which isolates the -4.

3) Reflection for Question #8 pg 605

This Question is: After 7 days of heavy rainstorms, the water level in a river peaked at 2.85 m above regular level. Four days later the water dropped to 2.25 m above the regular level.

This lesson we learned slope as a rate of change and it was one of the harder lessons for me. In the question the water was falling at a constant rate from the peak water level. For this question you needed to find a function that  describes the height of the river above regular level as a function of time. This means you needed to find the slope and create an equation of y = mx + b. Then you needed to figure out what the slope actually meant and this was easy for me because the water was just going down 0.15 m every day. I was confused when the question asked for the range and the domain. Then I realized that it was the peak water limit and when river has dried out. This question reminded me as the gas question because the amount kept on going down as time went on. I think I will have to study questions like this more before the test so that I completely understand them.

Math Journal

Question #3 pg. 479

The questions is Over the last 10 years, data was recorded for the number of cups of hot chocolate sold at the BGB Senior High School. It was found from the data that the water the day the less cups of hot chocolate were sold. The data can be modelled by the formula N t =150 – 10 t is the daily number of sups of hot chocolate sold the the average temperature is t C.

When I first read the problem I thought it was the same as all the other questions I had already anwnsered this assignment which it pretty much was but there was some different elements to it. To answer the questions you need to use the formula and input the (t). For this question you also need to be able to write the meaning of the function. When I was asked to explain the lower limit of the domain of the relation at first I was very confused. I thought it had to be a specific temperature but then I realized it was just the average minimum temperature. I learned when doing this question that all the questions may look  the same however their is different parts to them. I also learned to think outside the box. I think before the test I will need to study these types of questions and ask more questions about them. I will prepare myself by doing the practice test before the real test.

French Revolution Essay

The French revolution lasted from 1789-1795 and it was a time of fear, revolt and death. It affected almost everyone in France from the rich to the poor. The revolution also contributed to most of the rights and laws France still has today, France would not be the same without it. Throughout this time period there was many significant events contributing to the revolution but the most important ones were the Fall of Bastille, the Declaration of the Right of Man and the Reign of Terror.

The Fall of Bastille was the start of violence and this is what shaped the course of the revolution. Problems like poverty and the price of bread was not addressed. Riots started breaking out throughout Paris and other cities. This forced King Louis to send mercenary troops to France to restore peace, but this just made the people of France nervous, so they began to arm themselves. On July 14,1789 a mob attacked a prison fortress in Paris. This was called the Bastille and when troops were sent to eliminate the mob they joined them instead. The Bastille was then quickly captured. Several prisoners were let out and the mean prison governors head was paraded throughout Paris. Within weeks the Bastille was completely torn down, with all the gunpowder inside stolen. The fall of Bastille shaped the course of the revolution because it was the start of violence. Louis’s power as a monarch was slipping away. Also this fortress was traditionally used by French kings to imprison subjects that didn’t agree with them politically, making the Bastille a representation of the oppressive nature of the monarchy. Other significant events like the Great fear and National Assembly reforms also may have never happened without the influence from the Fall of Bastille. In conclusion this event showed that the king only had so much power over his people and it lead to the fall of a monarchy.

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A mob attacking the Bastille

Source: https://www.awesomestories.com/asset/view/French-Revolution-Storming-the-Bastille

The Declaration of the Right of Man and the Citizen had a long term effect on France that will lead the country for the future. This document set out basic laws the government should follow. It resembled the United States Declaration of Independence and it also contained ideas from the English philosopher John Locke and French philosophes Voltaire, Montesquieu and Rousseau. This Declaration guaranteed equality for all citizens, as well as freedom of speech, thought, religion, security and property. Overall this made the country more happy because now a peasant was a free man which increased the productivity of the country. Throughout the country wealth was spread, that resulted in higher standards of living. A person would not be punished for what they said and this caused more say in government (enlightenment thinkers). This component was mostly significant because of its long term effect that lead the country for the future.

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The Declaration of the Right of Man and the Citizen

Source: http://www.humanrights.com/what-are-human-rights/brief-history/declaration-of-human-rights.html

From 1793-1794 after the death of Louis XVI France was a republic lead by the committee of public safety, this time was known as the reign of terror. This was the most radical time in the revolution, even Girondist were imprisoned because they were now considered enemies of the revolution. There was no restrains on the power of the jacobins and France was a dictatorship led by Robespierre. The committee of public of safety passed harsh laws to eliminate any enemies of the revolution and around 30,000 people were sent to the guillotine by Robespierre who deeply believed in France and the revolution. This of course had a significant impact on France. Apart from all the deaths there was some benefits at the time like education, participation in government, taxes based on income and the metric system. This time will be remembered forever and the only way to stop it was, the execution of Robespierre himself. The government had finally realized they had gone way too far. To many innocent lives were taken during this time for unjustified reasons, that went against many of France’s freedoms. Finally the reign of terror was significant because of it’s impact on the country that resulted in many bloody tragedies.

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People being executed during the Reign of Terror

Source: http://www.britannica.com/event/Reign-of-Terror

The Fall of Bastille, The Declaration of the Right of man and the Reign of terror all played major roles in the French revolution. The revolution came with many gains, although there were several deaths, the good outweighed the bad. The revolution changed France’s future and without it France would not have as many freedoms as it does today.

V for Vendetta Question

Is V a more of a freedom fighter or terrorist?

Anytime you use violence against innocent peolple wether accidental or not, it is terrorism, but really there is a bigger picture behind this terrorism. V was living under the law of the British government, who were keeping people in seperate factions and hurting other racises. V wanted to create a rebellion against the government and he used terrorism to form this rebellion. He wanted to blow up the parliament. Inclusion I believe V is a freedom fighter because he wanted to bring down the government and convince the people to rule themselves.