In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square and others. Given a general quadratic equation of the form a x 2 + b x + c = 0 with x representing an unknown, a, b and c representing constants with a ≠ 0, the quadratic formula is: where the plus-minus symbol "±" indicates that the quadratic equation has two solutions. Written separately, they become: x 1 = − b + b 2 − 4 a c 2 a and x 2 = − b − b 2 − 4 a c 2 a Each of these two solutions is called a root of the quadratic equation. Geometrically, these roots represent the x values at which any parabola, explicitly given as y = a x 2 + b x + c, crosses the x -axis; as well as being a formula that yields the zeros of any parabola, the quadratic formula can be used to identify the axis of symmetry of the parabola, the number of real zeros the quadratic equation contains.
The quadratic formula may be written as: x = − b 2 a ± b 2 − 4 a c 4 a 2, which may be simplified to: x = − ± 2 − c a. This version of the formula is convenient when complex roots are involved, in which case the expression outside the square root will be the real part—and the square root expression the imaginary part; the expression inside the square root is a discriminant. A lesser known quadratic formula, used in Muller's method and which can be found from Vieta's formulas, provides the same roots via the equation: x = − 2 c b ± b 2 − 4 a c = 2 c − b ∓ b 2 − 4 a c; the standard parametrization of the quadratic equation is a x 2 + b x + c = 0. Some sources older ones, use alternative parameterizations of the quadratic equation such as a x 2 − 2 b 1 x + c = 0, where b 1 = − b / 2,or a x 2 + 2 b 2 x + c = 0, where b 2 = b / 2; these alternative parametrizations result in different forms for the solution, but which are otherwise equivalent to the standard parametrization. Many different methods to derive the quadratic formula are available in the literature.
The standard one is a simple application of the completing the square technique. Alternative methods are sometimes simpler than completing the square, may offer interesting insight into other areas of mathematics. Divide the quadratic equation by a, allowed because a is non-zero: x 2 + b a x + c a = 0. Subtract c/a from both sides of the equation, yielding: x 2 + b a x = − c a; the quadratic equation i
Kevin Kennedy is an English actor and musician, best known for playing the character Curly Watts for 20 years in ITV's long-running television soap opera Coronation Street. Kennedy was born in Manchester, he was a keen member of Manchester Youth Theatre. Kennedy studied drama at Manchester Polytechnic. Kennedy was in the band the Paris Valentinos with Andy Rourke. Between 1983-2003, Kennedy played the character of Norman "Curly" Watts in the TV soap Coronation Street. Among other jobs, the character started as a paperboy became a dustman, was an assistant manager at a supermarket; the character had two marriages. After a short break from acting whilst recovering from an alcohol addiction in 2000, he released a single, Bulldog Nation, with his band the Bunch of Thieves, on the RCA Records label; the single peaked at #70 on the UK Singles Chart. He returned to Coronation Street a few months before being written out permanently in September 2003. In an interview in 2009, Kennedy said that he would consider a return to the show and it was confirmed that he would film scenes for its fiftieth anniversary DVD.
However, more than a decade after his departure, he has yet to make a return. Kennedy was the producer of the 2005 television series Spanish Capers. A second series was recorded in 2006-07 for Sky Television plc. In 2009, Kennedy played the part of ageing hippie "Pop" in the touring production of Ben Elton's We Will Rock You before joining the cast of the West End London production in 2010. In 2015, Kennedy was asked to be involved with the launch of the world's third-largest cruise liner "Anthem of the Seas" appearing in a West End production of "We Will Rock You", he appeared in the 2009 "Scent from Heaven?" advert for Daz, as part of the company's "Cleaner Close" campaign. In 2010, along with several other Coronation Street stars, contributed to Trisha Ward's album Rogues, Angels and Fools, recorded for the fiftieth anniversary of the soap. In 2017, he played Graham Ollerinshaw, a David Bowie tribute act, in an episode of the BBC's Holby City, he is appearing this year, 2019, in Cinderella at Cambridge Arts Theatre, Cambridgeshire He has played a role in Mrs Brown's Boys playing an angel, in the Christmas Episode A Wonderful Mammy shown on 25 December 2019.
Kennedy has three children. A supporter of Manchester City, he serves as director of Kennedy St recovery services, a social enterprise, with his wife Clare, the Brighton-based organisation's CEO, offering free telephone advice, signposting to local recovery services, home-based detox, various recovery focused programs and a professional advice & coaching service to the business sector. Kevin Kennedy on IMDb
George Ericson, who worked under the name Eugene Iverd, was an American illustrator and painter. Iverd was born January 13, 1893 in St. Paul, he graduated from high school in Waseca, Minnesota, he received degrees from the Saint Paul School of Art and The Pennsylvania Academy of Fine Arts in Philadelphia. Iverd came to Erie, Pennsylvania, in September 1921 directly from the U. S. Army. In the army, he was an instructor at the Walter Reed Hospital in Washington, D. C. where he was located between August 1919 and July 1921. In the summer of 1921 he was hired as an art instructor at the Erie school district assigned to Academy High School, he is remembered fondly as an art instructor among his many successful students that were Joseph Plavcan, Wilbur Adams, Robert Joy, Andrew H. Hintenach, Lester Roesner, Harry Simpson; when he was at the Art Academy he sent many Erie Students to the Academy of Fine Arts at Philadelphia and at one time there was six of his students out of one hundred. He gave his time to the art classes until 1930.
In his career he designed a series of four calendars and he completed work for Erie Lithograph Co. and work for the U. S. Lithograph Co. in Brooklyn. Iverd was nationally known for the covers he painted for the Saturday Evening Post, McCall's, Ladies Home Journal, The American Magazine, he made several paintings for the Dorrance Co. Successful Farming, Christian Herald, The Rotarian, Monarch Foods, Winchester Western Company, Pure Oil Cooperation, Iodent Toothpaste and the Buffalo Evening News, he used the children of Erie as models for his works. Ericson remained in Erie and did not move to a Metropolitan area because he was assured of securing child models that had the "glow of sunshine in them"; as an illustrator, he shared an important accomplishment alongside artists as Grant Wood, Frederic Remington, Norman Wyeth, Andrew Wyeth, Norman Rockwell. They all had in common that they sold paintings to the Curtis Publishing Company that were used for covers on the Saturday Evening Post, he produced 29 covers for the Saturday Evening Post between 1926 and his death in 1936.
Many Erie children who posed for Ericson appeared on the cover of magazines and advertisements. He had a niche for capturing the joys and wholesomeness of boyhood and children were the subjects of many of his paintings. In 1930, George and Lillian Ericson purchased a plot in the Glenwood neighborhood of Erie, PA where he designed and had built a large house with five bedrooms, two and a half bathrooms, two fireplaces, three chimneys, many interesting features; the oak beams in the living room ceiling were imported from Canada, the walls were plastered in the French style, which Ericson demonstrated to the craftsmen building his house. The wooden doors inside the house are unusually shaped. One year after Ericson's sudden 1936 death, Mrs. Lillian Ericson sold the house to Richard and Katherine Yates, it has since changed hands six more times. In 2002, it underwent a major renovation and refurbishing and much of the original look was restored. Two of the Iverd paintings are still hanging in the house today, including "Fall" above the living room fireplace, as well as one of his Saturday Evening Post covers above the studio fireplace in the room he used for paintings.
In Erie there is a mural by Ericson in the Zem Zem Children's Hospital. A large collection of his work is at the Erie School Board at the Erie History Center
Louis Marcus HRHA is an Irish documentarian. Louis Marcus was born to an Irish Jewish family in Cork City in 1936, his brother David Marcus was a writer. Their grandfather, Louis Roseberg, arrived in Cobh, County Cork in 1882, from Akmenė fleeing persecution in the Russian Empire. Marcus won the Silver Bear for Best Short Film for Flea Ceoil at the 1967 Berlin International Film Festival. Children at Work was nominated for the Academy Award for Best Documentary at the 46th Academy Awards, while Conquest of Light was nominated for the Academy Award for Best Live Action Short Film at the 48th Academy Awards, he is an honorary member of the Royal Hibernian Academy. His sons Shimmy Marcus and Joe Marcus are filmmakers. Louis Marcus on IMDb
German submarine U-360 was a Type VIIC U-boat of Nazi Germany's Kriegsmarine during World War II. She carried out five patrols before being sunk in the Norwegian Sea by a British warship in April 1944, she was a member of five wolfpacks. She damaged one warship. German Type VIIC submarines were preceded by the shorter Type VIIB submarines. U-360 had a displacement of 769 tonnes when at the 871 tonnes while submerged, she had a total length of 67.10 m, a pressure hull length of 50.50 m, a beam of 6.20 m, a height of 9.60 m, a draught of 4.74 m. The submarine was powered by two Germaniawerft F46 four-stroke, six-cylinder supercharged diesel engines producing a total of 2,800 to 3,200 metric horsepower for use while surfaced, two AEG GU 460/8–27 double-acting electric motors producing a total of 750 metric horsepower for use while submerged, she had two 1.23 m propellers. The boat was capable of operating at depths of up to 230 metres; the submarine had a maximum submerged speed of 7.6 knots. When submerged, the boat could operate for 80 nautical miles at 4 knots.
U-360 was fitted with five 53.3 cm torpedo tubes, fourteen torpedoes, one 8.8 cm SK C/35 naval gun, 220 rounds, two twin 2 cm C/30 anti-aircraft guns. The boat had a complement of between sixty; the submarine was laid down on 9 August 1941 at the Flensburger Schiffsbau yard at Flensburg as yard number 479, launched on 28 July 1942 and commissioned on 12 November under the command of Oberleutnant zur See Hans-Jügen Bühring. She served with the 5th U-boat Flotilla from 12 November 1942 and the 13th flotilla from 1 July 1943; the boat's first patrol was preceded by trips from Kiel in Germany to Bergen and Narvik in Norway, from where she departed on 16 August 1943. She sailed west of Bear Island, she docked in Hammerfest on 24 September. Her second foray was a repeat of her first - finishing in Narvik on 19 November 1943; the submarine's third patrol took her around Bear Island. Sortie number four saw the boat damaging HMS Obdurate southeast of Bear Island on 25 January 1944, she damaged the Fort Bellingham the next day.
This ship was subsequently sunk by U-957. Having moved from Hammerfest to Trondheim, U-360 started her fifth patrol on 29 March 1944. On 2 April, she was sunk southwest of Bear Island by depth charges from the British destroyer HMS Keppel. 51 men died in the U-boat. U-360 took part in five wolfpacks, namely. Monsun Eisenbart Eisenbart Isegrim Blitz Helgason, Guðmundur. "The Type VIIC boat U-360". German U-boats of WWII - uboat.net. Retrieved 26 December 2014. Hofmann, Markus. "U 360". Deutsche U-Boote 1935-1945 - u-boot-archiv.de. Retrieved 26 December 2014
Splashgirl is a Norwegian jazz ensemble comprising the three young musicians Andreas Stensland Løwe, Jo Berger Myhre and Andreas Lønmo Knudsrød, playing original music. Since 2007, Splashgirl has released four acclaimed albums Doors. Keys. Arbor and Field Day Rituals, has played a great number of concerts in Europe, USA and Japan, collaborated with musicians like Sidsel Endresen, Jan Bang, Eyvind Kang, Mari Kvien Brunvoll, Randall Dunn and Timothy Mason. 2007: Doors. Keys. 2009: Arbor 2011: Splashgirl / Huntsville 2011: Pressure 2013: Field Day Rituals 2016: Hibernation Official website Splashgirl at All About Jazz