Upper airway resistance syndrome

Upper airway resistance syndrome
Other namesUARS, non-hypoxic sleep-disordered breathing

Upper airway resistance syndrome (UARS) is a sleep disorder characterized by the narrowing of the airway that can cause disruptions to sleep.[1][2] The symptoms include unrefreshing sleep, fatigue, sleepiness, chronic insomnia, and difficulty concentrating. UARS can be diagnosed by polysomnograms capable of detecting Respiratory Effort-related Arousals. It can be treated with lifestyle changes, functional orthodontics, surgery, mandibular repositioning devices or CPAP therapy.[3] UARS is considered a variant of sleep apnea,[4] although some scientists and doctors believe it to be a distinct disorder.[5][6]

History

Upper airway resistance syndrome was first recognized at Stanford University in the late 1980s. The article that described it by name, along with its relationship to obstructive sleep apnea, was published in 1992 by Guilleminault et al.[7]

Signs and symptoms

Symptoms of UARS are similar to those of obstructive sleep apnea, but not inherently overlapping. Fatigue, insomnia, daytime sleepiness, unrefreshing sleep, anxiety, and frequent awakenings during sleep are the most common symptoms. Oxygen desaturation is minimal or absent in UARS, with most having a minimum oxygen saturation >92%.[8]

Many patients experience chronic insomnia that creates both a difficulty falling asleep and staying asleep. As a result, patients typically experience frequent sleep disruptions.[9] Most patients with UARS snore, but not all.[4]

Some patients experience hypotension, which may cause lightheadedness, and patients with UARS are also more likely to experience headaches and irritable bowel syndrome.[9]

Predisposing factors include a high and narrow hard palate, an abnormally small intermolar distance, an abnormal overjet greater than or equal to 3 millimeters, and a thin soft palatal mucosa with a short uvula. In 88% of the subjects, there is a history of early extraction or absence of wisdom teeth. There is an increased prevalence of UARS in east Asians.[6]

Pathophysiology

Upper airway resistance syndrome is caused when the upper airway narrows without closing. Consequently, airflow is either reduced or compensated for through an increase in inspiratory efforts. This increased activity in inspiratory muscles leads to the arousals during sleep which patients may or may not be aware of.[1]

A typical UARS patient is not obese and possesses small jaws, which can result in a smaller amount of space in the nasal airway and behind the base of the tongue.[4] Patients may have other anatomical abnormalities that can cause UARS such as deviated septum, inferior turbinate hypertrophy, a narrow hard palate that reduces nasal volume, enlarged tonsils, or nasal valve collapse.[10][2] UARS affects equal numbers of males and females.[1]

Why some patients with airway obstruction present with UARS and not OSA is thought to be caused by alterations in nerves located in the palatal mucosa. UARS patients have largely intact and responsive nerves, while OSA patients show clear impairment and nerve damage. Functioning nerves in the palatal mucosa allow UARS patients to more effectively detect and respond to flow limitations before apneas and hypopneas can occur. Patients with intact nerves are able to dilate the genioglossus muscle, a key compensatory mechanism utilized in the presence of airway obstruction. What damages the nerves is not definitively known, but it is hypothesized to be caused by the long term effects of gastroesophageal reflux and/or snoring.[11][12]

Diagnosis

UARS is diagnosed using the Respiratory Disturbance Index (RDI). A patient is considered to have UARS when they have an Apnea-Hypopnea Index (AHI) less than 5, but an RDI greater than or equal to 5. Unlike the Apnea-Hypopnea Index, the Respiratory Disturbance Index includes Respiratory Effort-related Arousals (RDI = AHI + RERA Index).[13] In 2005, the definition of sleep apnea was changed to include patients with UARS by using RDI to determine sleep apnea severity.

The diagnosis of UARS is based on findings on a polysomnogram. On polysomnograms, a UARS patient will have very few apneas and hypopneas, but many Respiratory effort-related Arousals. Portable Home Sleep Test monitors (HST) are an alternative to sleep-laboratory polysomnography. Some of the HSTs allow for the breathing signals to be viewed within the raw data of the HST study and even a cursory review of these flow signals, will reveal those patients who would likely have upper airway resistance syndrome as well. RERAs are periods of increased respiratory effort lasting for more than ten seconds and ending in arousal. Whether or not an event is classified as a RERA or Hypopnea depends on the definition of Hypopnea used by the sleep technician.[13] The American Academy of Sleep Medicine currently recognizes two definitions. The scoring of Respiratory Effort-related Arousals is currently designated as "optional" by the AASM. Thus, many patients who receive sleep studies may receive a negative result, even if they have UARS.[14]

Based on symptoms, patients are commonly misdiagnosed with idiopathic insomnia, idiopathic hypersomnia, chronic fatigue syndrome, fibromyalgia, or a psychiatric disorder such as ADHD or depression.[9] Studies have found that children with UARS are frequently misdiagnosed with ADHD. One study found UARS or OSA present in up to 56% of children with ADHD.[15] Studies show that symptoms of ADHD caused by UARS significantly improve or remit with treatment in surgically treated children.[16]

Management

Behavioral modification

Behavioral modifications include getting at least 7–8 hours of sleep and various lifestyle changes, such as positional therapy.[17] Sleeping on one's side rather than in a supine position or using positional pillows can provide relief, but these modifications may not be sufficient to treat more severe cases.[17] Avoiding sedatives including alcohol and narcotics can help prevent the relaxation of airway muscles, and thereby reduce the chance of their collapse. Avoiding sedatives may also help to reduce snoring.[17]

Medications

Nasal steroids may be prescribed in order to ease nasal allergies and other obstructive nasal conditions that could cause UARS.[17]

Positive airway pressure therapy

If left untreated, UARS can develop into obstructive sleep apnea. Treatments for OSA such as positive airway pressure therapy can be effective at stopping the progression of UARS.[18][19] Positive airway pressure therapy is similar to that in obstructive sleep apnea and works by stenting the airway open with pressure, thus reducing the airway resistance. Use of a CPAP can help ease the symptoms of UARS. Therapeutic trials have shown that using a CPAP with pressure between four and eight centimeters of water can help to reduce the number of arousals and improve sleepiness.[4] CPAPs are the most promising treatment for UARS, but effectiveness is reduced by low patient compliance.[20]

Oral appliances

Oral appliances to protrude the tongue and lower jaw forward have been used to reduce sleep apnea and snoring, and hold potential for treating UARS, but this approach remains controversial.[20] Oral appliances may be a suitable alternative for patients who cannot tolerate CPAP.[17]

Surgery

For nasal obstruction, options can be septoplasty, turbinate reductions, or surgical palate expansion.[2]

Orthognathic surgeries that expands the airway, such as Maxillomandibular advancement (MMA) or Surgically Assisted Rapid Palatal Expansion (SARPE) are the most effective surgeries for sleep disordered breathing.

Though less common methods of treatment, various surgical options including uvulopalatopharyngoplasty (UPPP), hyoid suspension, and linguloplasty exist. These procedures increase the dimensions of the upper airway and reduce the collapsibility of the airway.[3] One should also be screened for the presence of a hiatal hernia, which may result in abnormal pressure differentials in the esophagus, and in turn, constricted airways during sleep.[3] Palatal tissue reduction via radiofrequency ablation has also been successful in treating UARS.[20]

Maxillary expansion

Orthodontic treatment to expand the volume of the nasal airway, such as nonsurgical Rapid Palatal expansion is common in children.[21][17] Due to the ossification of the median palatine suture, traditional tooth-born expanders cannot achieve maxillary expansion in adults as the mechanical forces instead tip the teeth and dental alveoli. Mini-implant assisted rapid palatal expansion (MARPE) has been recently developed as a minimally invasive option for the transverse expansion of the maxilla in adults.[22] This method increases the volume of the nasal cavity and nasopharynx, leading to increased airflow and reduced respiratory arousals during sleep.[23]

See also

References

  1. ^ a b c Shneerson, John M., ed. (2005). Sleep Medicine (Second ed.). New York: Blackwell Publishing. pp. 229-237.
  2. ^ a b c de Oliveira, Pedro Wey Barbosa; Gregorio, Luciano Lobato; Silva, Rogério Santos; Bittencourt, Lia Rita Azevedo; Tufik, Sergio; Gregório, Luis Carlos (July 2016). "Orofacial-cervical alterations in individuals with upper airway resistance syndrome". Brazilian Journal of Otorhinolaryngology. 82 (4): 377–384. doi:10.1016/j.bjorl.2015.05.015. PMC 9448996. PMID 26671020.
  3. ^ a b c de Godoy, Luciana B. M.; Palombini, Luciana O.; Guilleminault, Christian; Poyares, Dalva; Tufik, Sergio; Togeiro, Sonia M. (1 January 2015). "Treatment of upper airway resistance syndrome in adults: Where do we stand?". Sleep Science. 8 (1): 42–48. doi:10.1016/j.slsci.2015.03.001. PMC 4608900. PMID 26483942.
  4. ^ a b c d Cuelbras, Antonio (1996). Clinical Handbook of Sleep Disorders. New York: Butterworth-Heinemann. pp. 207.[page needed]
  5. ^ de Godoy, Luciana B.M. (20 March 2015). "Treatment of upper airway resistance syndrome in adults: Where do we stand?". Sleep Science. 8 (1): 42–48. doi:10.1016/j.slsci.2015.03.001. PMC 4608900. PMID 26483942.
  6. ^ a b Guilleminault, Christian; Chowdhuri, Susmita (May 2000). "Upper Airway Resistance Syndrome Is a Distinct Syndrome". American Journal of Respiratory and Critical Care Medicine. 161 (5): 1412–1413. doi:10.1164/ajrccm.161.5.16158a. PMID 10806128.
  7. ^ Guilleminault, Christian; Stoohs, Riccardo; Clerk, Alex; Simmons, Jerald; Labanowski, Michael (1992). "From Obstructive Sleep Apnea Syndrome to Upper Airway Resistance Syndrome: Consistency of Daytime Sleepiness". Sleep. 15 (S6): S13–S16. doi:10.1093/sleep/15.suppl_6.S13. PMID 1470801.
  8. ^ Bao, Gang; Guilleminault, Christian (November 2004). "Upper airway resistance syndrome-one decade later". Current Opinion in Pulmonary Medicine. 10 (6): 461–467. doi:10.1097/01.mcp.0000143689.86819.c2. PMID 15510051. S2CID 37248742.
  9. ^ a b c Kushida, Clete A., ed. (2009). Handbook of Sleep Disorders (Second ed.). New York: Inform Healthcare. pp. 339–347.
  10. ^ Garcha, Puneet S.; Aboussouan, Loutfi S.; Minai, Omar (January 2013). "Cleveland Clinic Sleep-Disordered Breathing". Virtual Medical School.
  11. ^ Guilleminault, Christian; Li, Kasey; Chen, Ning-Hung; Poyares, Dalva (September 2002). "Two-Point Palatal Discrimination in Patients With Upper Airway Resistance Syndrome, Obstructive Sleep Apnea Syndrome, and Normal Control Subjects". Chest. 122 (3): 866–870. doi:10.1378/chest.122.3.866. PMID 12226025.
  12. ^ Poothrikovil, Rajesh P.; Al Abri, Mohammed A. (May 2012). "Snoring Induced Nerve Lesions in the Upper Airway". Sultan Qaboos University Medical Journal. 12 (2): 161–168. doi:10.12816/0003108. PMC 3327562. PMID 22548134.
  13. ^ a b de Godoy, Luciana B.M.; Palombini, Luciana O.; Guilleminault, Christian; Poyares, Dalva; Tufik, Sergio; Togeiro, Sonia M. (January 2015). "Treatment of upper airway resistance syndrome in adults: Where do we stand?". Sleep Science. 8 (1): 42–48. doi:10.1016/j.slsci.2015.03.001. PMC 4608900. PMID 26483942.
  14. ^ Berry, Richard B.; Budhiraja, Rohit; Gottlieb, Daniel J.; Gozal, David; Iber, Conrad; Kapur, Vishesh K.; Marcus, Carole L.; Mehra, Reena; Parthasarathy, Sairam; Quan, Stuart F.; Redline, Susan; Strohl, Kingman P.; Ward, Sally L. Davidson; Tangredi, Michelle M. (15 October 2012). "Rules for Scoring Respiratory Events in Sleep: Update of the 2007 AASM Manual for the Scoring of Sleep and Associated Events: Deliberations of the Sleep Apnea Definitions Task Force of the American Academy of Sleep Medicine". Journal of Clinical Sleep Medicine. 08 (5): 597–619. doi:10.5664/jcsm.2172. PMC 3459210. PMID 23066376.
  15. ^ Huang, Yu-Shu; Chen, Ning-Hung; Li, Hsueh-Yu; Wu, Yu-Yu; Chao, Chia-Chen; Guilleminault, Christian (September 2004). "Sleep disorders in Taiwanese children with attention deficit/hyperactivity disorder". Journal of Sleep Research. 13 (3): 269–277. doi:10.1111/j.1365-2869.2004.00408.x. PMID 15339263. S2CID 19828868.
  16. ^ Amiri, Shahrokh; AbdollahiFakhim, Shahin; Lotfi, Alireza; Bayazian, Gholamreza; Sohrabpour, Mojtaba; Hemmatjoo, Taghi (August 2015). "Effect of adenotonsillectomy on ADHD symptoms of children with adenotonsillar hypertrophy and sleep disordered breathing". International Journal of Pediatric Otorhinolaryngology. 79 (8): 1213–1217. doi:10.1016/j.ijporl.2015.05.015. PMID 26066853.
  17. ^ a b c d e f "Upper Airway Resistance Syndrome (UARS)". Stanford Medicine. Retrieved February 28, 2017.
  18. ^ "Treatments". stanfordhealthcare.org. Retrieved 2021-05-11.
  19. ^ Repasky, David (2021-03-03). "CPAP Machine: How It Works, Reasons, and Uses". CPAP.com. Retrieved 2021-05-11.
  20. ^ a b c Exar, Elliott N.; Collop, Nancy A. (April 1999). "The Upper Airway Resistance Syndrome". Chest. 115 (4): 1127–1139. doi:10.1378/chest.115.4.1127. PMID 10208219.
  21. ^ Guilleminault, Christian; Khramtsov, Andrei (1 December 2001). "Upper airway resistance syndrome in children: A clinical review". Seminars in Pediatric Neurology. 8 (4): 207–215. doi:10.1053/spen.2001.29045. PMID 11768783.
  22. ^ Brunetto DP, Sant'Anna EF, Machado AW, Moon W (2017). "Non-surgical treatment of transverse deficiency in adults using Microimplant-assisted Rapid Palatal Expansion (MARPE)". Dental Press J Orthod. 22 (1): 110–125. doi:10.1590/2177-6709.22.1.110-125.sar. PMC 5398849. PMID 28444019.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  23. ^ Li, Qiming; Tang, Hongyi; Liu, Xueye; Luo, Qing; Jiang, Zhe; Martin, Domingo; Guo, Jing (1 May 2020). "Comparison of dimensions and volume of upper airway before and after mini-implant assisted rapid maxillary expansion". The Angle Orthodontist. 90 (3): 432–441. doi:10.2319/080919-522.1. PMC 8032299. PMID 33378437.

Read other articles:

Erik StrandmarkStrandmark dan Harriet Andersson dalam Woman in a Fur Coat (1958).LahirErik Alfred Strandmark(1919-09-14)14 September 1919Torsåker, SwediaMeninggal5 Januari 1963(1963-01-05) (umur 43)Trinidad dan TobagoKebangsaanSwediaPekerjaanPemeran, sutradara, penulis naskahTahun aktif1944–1962Suami/istriBernadine Philip Naturnee ​ ​(m. 1948)​ Erik Alfred Strandmark (14 September 1919 – 5 Januari 1963) adalah seorang pemeran fi...

 

إرنست ياكوبي (بالألمانية: Ernst Jacobi)‏    معلومات شخصية اسم الولادة (بالألمانية: Ernst Gerhard Ludwig Jacobi-Scherbening)‏  الميلاد 11 يوليو 1933 [1]  برلين  الوفاة 23 يونيو 2022 (88 سنة) [2]  فيينا  مواطنة ألمانيا  الحياة العملية التلامذة المشهورون إريك شافنر  [لغات أخرى]&#...

 

Un frein par compression est un dispositif qui agit sur les soupapes d’un moteur Diesel pour améliorer l'effet du frein moteur. Ce dispositif laisse les soupapes d'échappement partiellement ouvertes pendant les quatre temps du moteur, réduisant la compression de l'air et empêchant ainsi le gazole de s'enflammer, bien que l'injection de carburant ne soit pas suspendue. Types de freins à compression Il existe plusieurs fabricants de freins par compression dont les « freins Jacobs&#...

Pour les autres articles nationaux ou selon les autres juridictions, voir Assemblée nationale. Pour les autres articles nationaux ou selon les autres juridictions, voir Assemblée constituante. Pour les articles homonymes, voir Assemblée nationale constituante et Assemblée nationale française (homonymie). Assemblée nationale constituante 9 juillet 1789-30 septembre 1791 2 ans, 2 mois et 21 joursÀ gauche : Pavillon royalÀ droite : Emblème de l'Assemblée natio...

 

Buddhist monastic order in Myanmar Maha Dwara Nikaya (Burmese: မဟာဒွာရနိကာယ, IPA: [məhà dwàɹa̰ nḭkàja̰]); also spelt Maha Dwaya Nikaya or Mahādvāra Nikāya, is a small monastic order of monks in Myanmar (Burma), primarily in Lower Myanmar.[1] This order is very conservative with respect to Vinaya regulations.[2] It is one of 9 legally sanctioned monastic orders (nikaya) in the country, under the 1990 Law Concerning Sangha Organization...

 

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: WJKE – news · newspapers · books · scholar · JSTOR (August 2012) (Learn how and when to remove this message) Radio station in Stillwater, New YorkWJKEStillwater, New YorkBroadcast areaSaratoga County, Capital RegionFrequency101.3 MHzBrandingK-LoveProgrammingFor...

Questa voce o sezione sull'argomento militari statunitensi non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Segui i suggerimenti del progetto di riferimento. Daniel Harvey HillNascitaHill's Iron Works, 12 luglio 1821 MorteCharlotte, 24 settembre 1889 Dati militariPaese servito Stati Uniti Stati Confederati d'America Forza armata United States...

 

この項目には、一部のコンピュータや閲覧ソフトで表示できない文字が含まれています(詳細)。 数字の大字(だいじ)は、漢数字の一種。通常用いる単純な字形の漢数字(小字)の代わりに同じ音の別の漢字を用いるものである。 概要 壱万円日本銀行券(「壱」が大字) 弐千円日本銀行券(「弐」が大字) 漢数字には「一」「二」「三」と続く小字と、「壱」「...

 

LioAta Li'oPeta sebaran kelompok etnis dan bahasa di Pulau Flores dan pulau-pulau kecil sekitarnya.Jumlah populasi300.000 (1998)[1]Daerah dengan populasi signifikanPulau Flores (Ende dan Sikka)BahasaLio, Ende, IndonesiaAgamaMayoritas Katolik, minoritas IslamKelompok etnik terkaitEnde • Sikka • Nage Suku Lio (Ata Li'o) adalah kelompok etnis yang mendiami Pulau Flores bagian tengah. Masyarakat suku Lio pada umumnya mendiami wilayah kecamatan Wolowaru, Ndona, Ndona Timur, D...

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Desember 2023. Benjamin Corgnet Informasi pribadiNama lengkap Benjamin CorgnetTanggal lahir 6 April 1987 (umur 37)Tempat lahir Thionville, PrancisTinggi 180 m (590 ft)Posisi bermain GelandangInformasi klubKlub saat ini LorientNomor 7Karier junior1998...

 

كأس العالم لكرة القدم 2006 (بالإنجليزية: 2006 FIFA World Cup)‏  الغلاف البريطاني للعبة فيفا كأس العالم المطور إي أيه كندا بلاي ستيشن بورتبل الناشر إي أيه سبورتس سلسلة اللعبة ألعاب فيديو كأس العالم لكرة القدم النظام جيم بوي أدفانس نينتندو جيم كيوب نينتندو دي إس إكس بوكس مايكروسوفت ...

 

Railway station in west Wales PantyffynnonGeneral informationLocationPantyffynnon, CarmarthenshireWalesCoordinates51°46′44″N 3°59′49″W / 51.779°N 3.997°W / 51.779; -3.997Grid referenceSN622107Managed byTransport for WalesPlatforms2Other informationStation codePTFClassificationDfT category F2Key dates1841OpenedPassengers2018/19 3,6322019/20 3,4422020/21 822021/22 1,4282022/23 2,404 Listed Building – Grade IIFeaturePantyffynnon Railway StationDesignated12 M...

1751-52 siege of Trichinopoly during the Second Carnatic War This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (September 2014) (Learn how and when to remove this message) Siege of TrichinopolyPart of the Second Carnatic WarMap of Trichinopoly During Second Carnatic WarDateJuly 1751 – 10 April 1752LocationTiruchirappalli, modern-day Tamil NaduResult British - ...

 

У этого термина существуют и другие значения, см. Шарлотта Амалия. ГородШарлотта-Амалияангл. Charlotte Amalie 18°21′ с. ш. 64°57′ з. д.HGЯO Страна  США Штат Американские Виргинские острова История и география Основан 1666 Площадь 3.14 км² Высота центра 0 м Часовой пояс UTC&...

 

Gerard 't HooftNovember 2008Lahir5 Juli 1946 (umur 78)Den Helder, BelandaKebangsaanBelandaAlmamaterUniversitas UtrechtDikenal atasTeori medan kuantum, Gravitasi kuantumPenghargaanPenghargaan Wolf (1981)Medali Lorentz (1986)Penghargaan Spinoza (1995)Medali Franklin (1995)Penghargaan Nobel Fisika (1999) Medali Emas Lomonosov (2010)Karier ilmiahBidangFisika TeoretisInstitusiUniversitas UtrechtPembimbing doktoralMartinus J. G. VeltmanMahasiswa doktoralRobbert DijkgraafHerman Verlinde Gerard...

College football team representing the United States Air Force Academy Air Force Falcons football2024 Air Force Falcons football team First season1955; 69 years agoAthletic directorNathan PineHead coachTroy Calhoun 17th season, 129–82 (.611)StadiumFalcon Stadium(capacity: 56,409)Field surfaceTurfLocationAir Force Academy, Colorado, U.S.NCAA divisionDivision I FBSConferenceMountain West (1999–present)DivisionMountain (2013–2019; 2021–2022)Past conferencesIndependent (1955)Universi...

 

ポール・リビア ポール・リビア(英: Paul Revere、1735年1月1日 - 1818年5月10日)は、アメリカ、マサチューセッツ湾植民地出身の銀細工師であり、アメリカ独立戦争中は愛国者として活動した。ポール・リヴィアとも。 レキシントン・コンコードの戦いにおける伝令の役割を担ったことで、リビアはその死後も不朽の名声を与えられ、リビアの名前と「真夜中の騎行」と...

 

Political, economic or military predominance of one state over other states Hegemon redirects here. For other uses, see Hegemon (disambiguation). Ancient Greece under the hegemony of Thebes, 371–362 BC Hegemony (/hɛˈdʒɛməni/ ⓘ, UK also /hɪˈɡɛməni/, US also /ˈhɛdʒəmoʊni/) is the political, economic, and military predominance of one state over other states, either regional or global.[1][2][3] In Ancient Greece (ca. 8th BC – AD 6th c.), hegemony d...

Italian bicycle manufacturer 45°41′54″N 12°15′11″E / 45.6982616°N 12.2529689°E / 45.6982616; 12.2529689 PinarelloTrade namePinarelloCompany typePrivateIndustryBicycle industryFounded1953; 71 years ago (1953), TrevisoFounderGiovanni PinarelloHeadquartersTreviso, ItalyArea servedWorldwideProductsBicycles, E-bike and related componentsParentPrivate Family OfficeWebsitepinarello.com Cicli Pinarello S.p.A. is an Italian bicycle manufacturer bas...

 

Method for solving quadratic equations Animation depicting the process of completing the square. (Details, animated GIF version) In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form a x 2 + b x + c {\displaystyle ax^{2}+bx+c} to the form a ( x − h ) 2 + k {\displaystyle a(x-h)^{2}+k} for some values of h and k. In other words, completing the square places a perfect square trinomial inside of a quadratic expression. Completing the...