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Answer: In Exercises 61 to 64, find the vertex of the

College Algebra and Trigonometry | 7th Edition | ISBN: 9781439048603 | Authors: Richard N. Aufmann ISBN: 9781439048603 155

Solution for problem 63 Chapter 2

College Algebra and Trigonometry | 7th Edition

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College Algebra and Trigonometry | 7th Edition | ISBN: 9781439048603 | Authors: Richard N. Aufmann

College Algebra and Trigonometry | 7th Edition

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Problem 63

In Exercises 61 to 64, find the vertex of the graph of the quadratic function.

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Music Appreciation notes of April 5-7 April 5 • Richard Wagner • German. He was Hitler’s idol as a musician. As a young man he was part of a group that became the Nazis. Because of this he was forced to go into exile. He believed the German race was smarter than anyone else. he came up with the design of a modern concert hall/ opera house and theatrical lighting. He wrote “The bridal march.” He increased the size of the Opera by half, so that is why they had to sing so loud • synonymous with opera. They were based on Germanic legends/folklores. They are very difficult to stage because of huge casts, sets, and very expensive Lohengrin—takes place in Middle Ages in Belgium about a king killed in battle who leaves • his son and daughter at the kingdom. Ortrude is an evil witch woman who wants to seize control of the kingdom by getting away with both the son and daughter, Elsa. So she casts a spell on the son to turn him into a swan and goes to the village to tell them Elsa killed him so she could gain the throne and accuses Elsa of murder. They take her to the place of justice and decide to use the traditional way to see if she is guilty. The accused would be in the middle and would fight the accuser and whoever won would be innocent. Women could choose a defender so Ortrude uses a spell to make an ogre and Elsa is terrified. The night before the fight, Elsa has a dream about a bird that is a swan and drops a bell on a single string in her palm. She felt the necklace when she woke up, and heard “in time of trouble, ring the bell.” So they are about to fight the ogre and uses the bell and through all of the mist, a boat appears that looks like a swan and off the boat steps a knight who is beautiful and tells her that he is there to defend her. The battle begins and the knight kills the ogre, and Elsa is innocent. Ortrude hides and Elsa falls in love and makes plans to be married. The music for the wedding scene is what we use today. On the night of their wedding, Elsa goes to the knight and asks for his name. And he said she can’t ask him that question because if she did, it would break the spell and he would have to leave. She was okay with this until Ortrude gets in her head and finally Elsa comes to the knight asking his name again. He tells her he is sorry because he has to leave now but he would answer her question. His name is Lohengrin and he is the knight who guards the Holy Grail. Now he has to go back for eternity. All the townspeople go back to the river, knights step on the boat and says goodbye. After the boat leaves, Elsa sees a swan go under water and it doesn’t come back up. She is worried so she goes down to save it and pulls out her brother. They rule the kingdom forever. • The Flying Dutchman—a ghost story. Among sailors it is an omen. In mythology, the people who make a living on the sea believe it was a ship in full sail without one person on board. It was completely empty of people. To this day, the people who live on the sea would tell you that they have seen the flying dutchman and that means that their ship is doomed. • Frederic Chopin (show pan) • Polish. He is synonymous to piano music. He loved teaching but piano was his thing. he wrote the “Funeral march” which was a sonata. By the romantic period the pianos look like what we have as a grand piano. He died in Paris of tuberculosis. He quit composing when his relationship ended Peter Ilyich Tchaikovsky • • Russian. Now we hear from composers all over the world. He studied law because his father didn’t want him to become a musician. He was extremely tortured because of his homosexuality and had numerous suicide attempts. He probably died from one of his attempts. When he jumped into the river, he probably drank some and developed cholera which comes form contaminated water. He was supported by Madame Von Meck (his patron). He wrote Swan Lake, Nutcracker. He was a personal friend of Nicholas. He performed at the premier at Carnegie Hall for $25,000 in 1891. He wrote a piece when the Russians defeated Napoleon, an overture and in it he shows peasant life in Russia, some fragments from the French and Russian anthems and he wrote this piece to be performed outside • Franz Liszt • also known for piano music. He took the piano and turned it into a concert instrument Impressionist period • painters like Monet and Van Gough (Starry Night only sold about $50 worth when he was alive but now it goes for 30 million dollars • In Paris at an exhibition in the late 1800s there was an incident where someone went to the exhibit, looked at the paintings and then left and committed suicide because he thought people were crazy • Instead of painting a picture of something, people told us what they thought/saw. Musicians decided to use instruments as colors and used it to describe their feelings. • The movement began in Paris near the end of the 19th century. It “melted” into the 20th century leaving a major influence on what was to come. The musicians during this period still has an impression on our music today The Impressionist idea Abstractionism • • Expressionism • Claude Debussy (1862-1918) • born in Paris. he was a momma’s boy and was raised by her • Began piano lessons at an early age • Entered Paris Conservatory at age 11. That would be like an 11yr old walk into our college class • Considered to be the father of impressionist movement • Debussy saw a beautiful young woman walking down the street and he was so inspired, he went back and composed music about her. Paints us an image of a woman walking down a street On our listening guide he writes the prelude of a faun. He is painting an image of this faun • who is seen in the clearing in the forest. He uses a flute solo and the harp • There are also now photos of actual people instead of paintings April 7 • in music, the word “classical” has two meanings—a period of time or the overall term of music, like in genres. ex. “Classic Rock” • Maurice Ravel (1875-1937) • considered to be one of the two great Impressionist composers because of the way he performed and the way he sounded • Born in France in a musical family Attended Paris Conservatory but was not treated well by the more “traditional” faculty • • Liked to experiment with musical forms and in doing so influenced many 20th century composers • Ravel was a composer that not many people believed in “Bolero” was his greatest piece; for years it has had a sexual connotation, they used it • during sexual scenes in movies. He used imitation/repetition; the snare drum plays the same beat the entire song. It was one of the 1st pieces of classical music that used the saxophone in the orchestra • Igor Stravinsky (1882-1971) • He was the result of the impressionist periods; not one of the two greatest • Russian, father didn’t want him to study music • He orchestrated Russian folk tales such as the “fire bird” • When he was 20, the Russian Revolution occurred so he went to America to become a resident and then to become a citizen • The firebird=the phoenix, it consumes itself in flames to be reborn again Composed almost to the end of his life • • The “Rite of Spring” was about pagan rituals; was a ballet and was controversial because they had to do it nude, the people didn’t like the way he conducted it or that it was toward the pagans (human sacrifices) • In the 20th Century, Martha Gram wrote down the dance moves for ballet; and we still use them today • Stravinsky was the effect of the impressionist era Some Great American Composers • Scott Joplin (1867-1917) • Rag-time musician. 1st recognized black composer he had no formal training • • Aaron Copland (1900-1990) • Incorporated many American folk songs into his compositions • He was a conductor, a teacher, writer and composer • Famous works: • “Fanfare for the Common Man”: only brass and percussion play this because it was meant to be played outside rain or shine. Wrote it for the tomb of the unknown soldier. • “Appalachian Spring”: he took the Shaker hymn “Simple Gifts” and turned it into this ballet. Tells the story of a young couple who go to the west to start a new life and tells us the troubles they face along the way • Born in Brooklyn American Musical Theater • Something original to America. What we can call our own in the musical industry

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Textbook: College Algebra and Trigonometry
Edition: 7
Author: Richard N. Aufmann
ISBN: 9781439048603

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Answer: In Exercises 61 to 64, find the vertex of the