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Özellikle f(a+1) fonksiyonunun grafiğini bir birim sola ötelediği ve bu durumda x eksenini kesen noktaların nasıl değiştiği ve köklerinin toplamının nasıl hesaplanacağı konuları üzerinde durulmaktadır."]},"endTime":775,"title":"Fonksiyon Uygulamaları ve Grafikleri Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyonel Uygulamalar","list":{"type":"unordered","items":["Murat Hoca, Yanıt Yayınları'nın kitap çözümüne başlıyor ve ilk konu olarak fonksiyonel uygulamaları ele alıyor.","Bir grafiğin fonksiyon olup olmadığını kontrol etmek için y eksenine paralel doğrular çekilir; eğer doğrular grafiği sadece bir noktada kesiyorsa grafik fonksiyondur.","Fonksiyonun tanım kümesi, x ekseninde nerede başlayıp nerede bittiğini gösterir; başlangıç ve bitiş noktaları dolu ise o noktalar tanım kümesine dahil edilir."]},"beginTime":0,"endTime":240,"href":"/video/preview/15812237026273886048?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=0&ask_summarization=1"},{"index":1,"title":"Fonksiyon Değerleri ve Ters Fonksiyonlar","list":{"type":"unordered","items":["Fonksiyonun kökleri, x eksenini kesen noktalardır; fonksiyonun y eksenini kesen noktası ise f(0) değeridir.","Ters fonksiyon bulmak için, y ekseninde istenen değeri bulup, o değeri takip ederek x eksenine gelinir.","Parçalı fonksiyonlarda, x yerine yazılması durumunda dolu noktaya gidilmelidir; boş noktaya gidilirse fonksiyon tanımsız olur."]},"beginTime":240,"endTime":521,"href":"/video/preview/15812237026273886048?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=240&ask_summarization=1"},{"index":2,"title":"Fonksiyon Dönüşümleri","list":{"type":"unordered","items":["y = f(x) + a fonksiyonu, f(x) fonksiyonunu a birim sola öteler.","Fonksiyonun kökleri, x eksenini kesen noktalardır; ters fonksiyonun kökleri ise y eksenini kesen noktalardır.","Fonksiyonun kökleri toplamı, x eksenini kesen noktaların toplamıdır."]},"beginTime":521,"endTime":670,"href":"/video/preview/15812237026273886048?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=521&ask_summarization=1"},{"index":3,"title":"Fonksiyon Grafiği ve Öteleme","list":{"type":"unordered","items":["Verilen f(x) fonksiyonunun grafiğinde x yerine a yazıldığında yeni bir fonksiyon elde edilir.","f(a+1) ifadesi, grafiğin bir birim sola ötelenmesini ifade eder.","Grafiğin sola ötelenmesiyle x eksenini kesen noktalar da bir birim sola kayar."]},"beginTime":675,"endTime":714,"href":"/video/preview/15812237026273886048?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=675&ask_summarization=1"},{"index":4,"title":"Köklerin Bulunması","list":{"type":"unordered","items":["x eksenini kesen noktalar, fonksiyonun köklerini temsil eder.","f(a+1) fonksiyonunun kökleri -4 ve -3'tür.","Sorunun cevabı, bu köklerin toplamıdır."]},"beginTime":714,"endTime":729,"href":"/video/preview/15812237026273886048?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=714&ask_summarization=1"}],"linkTemplate":"/video/preview/15812237026273886048?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Yanıt yayınları ayt matematik soru bankası çözümleri(sayfa 9-10)","related_orig_text":"Yanit Group","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Yanit 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video da yanıt yayınları ayt matematik soru bankası nın 1. ünitesi nin 5. testini çözdüm. erişemiyordum.Bu kanal aracılığıyla hem bu eksiğimi kapayıp hem kendi öğrencilerime konuları bir kez...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2387358/4285780f40295bb463071806bdb59e14/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/EPj3DAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=videoid:3724940191281319514","teaser":[{"list":{"type":"unordered","items":["Bu video, Murat Hoca tarafından sunulan bir matematik eğitim içeriğidir. Öğretmen, Yanıt Yayınları'nın beşinci testindeki soruları çözmektedir.","Videoda ikinci dereceden denklemler ve paraboller konusu ele alınmaktadır. İçerik, parabolün kollarının yönüne göre katsayıların işaretlerini, tepe noktasının x koordinatını, kökler çarpımını ve parabolün x ve y eksenlerini kestiği noktaları bulma yöntemlerini kapsamaktadır. Ayrıca üçgen alan hesaplamaları, simetri eksenini hesaplama ve kare alan hesaplamaları gibi konular da adım adım açıklanmaktadır.","Video, beş farklı sorunun çözümünü içermekte ve her soru için detaylı çözüm yöntemleri sunulmaktadır. Parabol denklemlerinde bilinmeyenleri bulma, köklerin hesaplanması ve alan hesaplamaları gibi konular detaylı olarak ele alınmaktadır."]},"endTime":851,"title":"Matematik Dersi: İkinci Dereceden Denklemler ve Paraboller","beginTime":0}],"fullResult":[{"index":0,"title":"İkinci Dereceden Fonksiyonların Parametreleri","list":{"type":"unordered","items":["Murat Hoca, Yanıt Yayınları'nın beşinci testinde ikinci dereceden fonksiyonların parametreleri (a, b, c) ile ilgili soruları çözüyor.","Parabol, ikinci dereceden denklemin grafiği (f(x) = ax² + bx + c) olarak tanımlanıyor.","Parabolün kolları aşağı doğruysa, x² katsayısı (a) negatif olmalıdır."]},"beginTime":0,"endTime":50,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=0&ask_summarization=1"},{"index":1,"title":"Tepe Noktası ve Kökler İlişkisi","list":{"type":"unordered","items":["Tepe noktasının x koordinatı (r) formülü -b/2a'dır ve tepe noktası x ekseni üzerindeyse r değeri pozitiftir.","Parabol x ekseni iki farklı noktada kesiyorsa, delta (Δ) değeri sıfırdan büyük olmalıdır (Δ = b² - 4ac > 0, c > 0, a \u003c 0)","Kökler çarpımı formülü c/a'dır ve kökler x ekseni üzerinde farklı noktalarda kesiyorsa, kökler çarpımı negatif olacaktır."]},"beginTime":50,"endTime":139,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=50&ask_summarization=1"},{"index":2,"title":"Fonksiyon Grafiği Soruları","list":{"type":"unordered","items":["İkinci soruda, parabolün kolları yukarı doğruysa a değeri pozitiftir.","Tepe noktasının x koordinatı negatif ise, r değeri negatif olur ve b/2a değeri pozitiftir.","Kökler çarpımı c/a formülü kullanılarak c değeri de pozitif olarak bulunur."]},"beginTime":139,"endTime":213,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=139&ask_summarization=1"},{"index":3,"title":"Fonksiyon Denklemleri ve Kesişim Noktaları","list":{"type":"unordered","items":["Fonksiyonun x ekseni kesen noktaları bulmak için fonksiyon sıfırlanır ve çarpanlara ayrılır.","Y eksenini kesen nokta bulmak için x yerine 0 denklemine yazılır.","Fonksiyonun x eksenini kesen noktaları ve y eksenini kesen noktası toplamı hesaplanır."]},"beginTime":213,"endTime":301,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=213&ask_summarization=1"},{"index":4,"title":"Parabollerin Y Eksenini Kesme Noktası","list":{"type":"unordered","items":["Parabollerin y eksenini aynı noktada kestiği durumda, x yerine 0 denklemine yazılır.","Parabollerin y eksenini kestiği nokta (0, a) noktasıdır.","Parabollerin y eksenini kestiği nokta formülü kullanılarak m+n değeri bulunur."]},"beginTime":301,"endTime":378,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=301&ask_summarization=1"},{"index":5,"title":"Parabol İçinde Geometrik Şekil","list":{"type":"unordered","items":["Parabolün içinde geometrik bir şekil sorulduğunda, önce geometrik şeklin alanını bulmak gerekir."]},"beginTime":378,"endTime":398,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=378&ask_summarization=1"},{"index":6,"title":"Üçgende Alan Hesaplama","list":{"type":"unordered","items":["Üçgende alan hesaplaması için taban çarpı yükseklik bölü iki formülü kullanılır.","Üçgenin taban uzunluğu için x ekseni kesen nokta (kök) ve y ekseni kesen nokta gereklidir.","Fonksiyonun x eksenini kesen noktası -1'den geçtiği bilgisi kullanılarak k değeri 4 olarak bulunur."]},"beginTime":399,"endTime":474,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=399&ask_summarization=1"},{"index":7,"title":"Fonksiyonun Çözümü","list":{"type":"unordered","items":["Fonksiyon x² + 3x + 4 olarak temizlenir.","Y eksenini kesen nokta için x=0 yazıldığında y=4 olarak bulunur.","X eksenini kesen noktalar (kökler) için denklem çarpanlarına ayrılır ve x=-1 ve x=4 olarak bulunur."]},"beginTime":474,"endTime":547,"href":"/video/preview/3724940191281319514?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=474&ask_summarization=1"},{"index":8,"title":"Üçgen Alanı Hesaplama","list":{"type":"unordered","items":["Üçgenin taban uzunluğu 4 birim olarak bulunur.","Üçgenin yüksekliği 5 birim olarak hesaplanır.","Üçgenin alanı 5×4÷2=10 birim kare olarak 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Yeşili bu bölümünde Muffin ajanının ağır sabotajı altında video çekmek zorunda kaldım :D Yılbaşı kaktüsü bakımı ile ilgili aşağıdaki konuları videoda bulabilirsiniz: Yılbaşı kaktüsü latince...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2039185/330a0a8c14e1e383a61ad8c3a643bef8/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/2XmqVwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=videoid:17039099809687588156","teaser":[{"list":{"type":"unordered","items":["Bu video, Gizem adlı bir bitki uzmanının \"Ev Yeşili\" kanalında sunduğu bir eğitim içeriğidir. Gizem, yılbaşı kaktüsünün (Schlumbergera bridgesi) bakımını detaylı olarak anlatmaktadır.","Video, yılbaşı kaktüsünün genel bilgileriyle başlayıp (Brezilya'nın tropik yağmur ormanlarından geldiği, kumlu topraktan hoşlandığı, çiçeklenme dönemleri) bakım detaylarına geçiyor. Gizem, bitkinin sulama, gübreleme, ışık gereksinimleri, dinlenme dönemleri ve çoğaltılması gibi konuları adım adım açıklıyor. Özellikle kasım-ocak çiçeklenme dönemi, şubat-nisan dinlenme dönemi ve yaz aylarında balkona çıkarma gibi önemli bakım dönemleri vurgulanıyor."]},"endTime":597,"title":"Yılbaşı Kaktüsü Bakım Rehberi","beginTime":0}],"fullResult":[{"index":0,"title":"Yılbaşı Kaktüsü Hakkında Genel Bilgi","list":{"type":"unordered","items":["Yılbaşı kaktüsü (Schlumbergera bridgesi) Brezilya'nın tropik yağmur ormanlarından gelen, nemli bir ortamdan gelen bir bitkidir.","Schlumbergera cinsinde altı ile sekiz arasında tür mevcuttur ve bu kaktüs üreticisi Frederick Schlumberger'den adını almıştır.","Yılbaşı kaktüsü genişliği otuz santime kadar uzanabilen, kumlu topraktan hoşlanan bir türdür."]},"beginTime":0,"endTime":89,"href":"/video/preview/17039099809687588156?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=0&ask_summarization=1"},{"index":1,"title":"Toprak ve Sulama Bakımı","list":{"type":"unordered","items":["Yılbaşı kaktüsü çok fazla su tutan, drenajı yüksek olmayan topraktan hoşlanmaz, torfun içerisinde dere kumu, kum ve inşaat kumu karıştırılmalıdır.","Toprağın üst kısmının kurumasını ister, tamamen kurumasını istemez; sulama zamanı toprağın üst kısmının kuru hissetmesi veya saksının hafif gelmesi ile anlaşılır.","Delikli saksıda olmalı, fazla su altından akmalı ve tabaktaki su en fazla yarım saat durduktan sonra boşaltılmalıdır."]},"beginTime":89,"endTime":216,"href":"/video/preview/17039099809687588156?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=89&ask_summarization=1"},{"index":2,"title":"Çiçeklenme ve Dinlenme Dönemi","list":{"type":"unordered","items":["Yılbaşı kaktüsü kasım başında başlayıp ocak sonuna kadar bir kere çiçeklenir, çiçekler döküldükten sonra şubat başından sonra bir iki ay dinlenme dönemi vardır.","Dinlenme döneminde 15-18 derece sıcaklık çevresinde serin bir yerde olmalı ve çok fazla sulama yapılmamalıdır.","Nisan ayına geldiğinde kaktüs besini ayda bir kez suyuna ekleyerek ağustos ortasına kadar düzenli olarak gübrelenmelidir."]},"beginTime":216,"endTime":305,"href":"/video/preview/17039099809687588156?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=216&ask_summarization=1"},{"index":3,"title":"Çiçeklenme Teşvik Etme ve Tomurcuklanma Dönemi","list":{"type":"unordered","items":["Eylül'e geldiğinde çiçeklenmeye teşvik etmek için dört-altı hafta boyunca tam gün uzunluğu yaşaması gerekir (günün 12-14 saatinde karanlık olması).","Eylül başı geldiğinde yazın balkonda olan yılbaşı kaktüsü içeriye alınmalı, 10 derece sıcaklığın altında mutlu olmayacaktır.","Tomurcukları gördükten sonra sulaması azaltılmalı, gübre vermeyi durdurulmalı ve yer değiştirilmemelidir."]},"beginTime":305,"endTime":411,"href":"/video/preview/17039099809687588156?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=305&ask_summarization=1"},{"index":4,"title":"Tomurcuklanma Döneminde Dikkat Edilmesi Gerekenler","list":{"type":"unordered","items":["Tomurcukları gördükten sonra gübreleme yapılmamalı ve yer değiştirilmemelidir.","Isı kaynaklarına (radyatör, soba, kalorifer) yakın olmak istemeyecektir, yerini değiştirirseniz veya toprağını fazla kurutursanız tomurcukları dökülebilir.","Kapalı balkonda veya normal balkonda bitkinin yanında bir bardağın içerisine su koyarak nemini düzenleyebilirsiniz."]},"beginTime":411,"endTime":495,"href":"/video/preview/17039099809687588156?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=411&ask_summarization=1"},{"index":5,"title":"Toprak Saksı Değişimi ve 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Sorularınızı yorumlara bekliyorum...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3009500/8c4e34b16adc5d12f141b7bf653169fc/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/0AOgMAIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=videoid:17632503169353800360","teaser":[{"list":{"type":"unordered","items":["Bu video, Educraft şirketinin temsilcisi olan bir konuşmacının doğa yürüyüşü sırasında Almanya'da şirket kurma ve oturum alma konusunda bilgi verdiği bir eğitim içeriğidir.","Video, Almanya'da şirket kurma sürecini, farklı şirket türlerini (UG, Gmbh, AG) ve yatırımcı vizesi başvurusu için gerekli koşulları detaylı şekilde anlatmaktadır. Konuşmacı, şirket kurmanın Avrupa'ya iş yapma imkanı sağladığını, oturum alma için minimum 50-100 bin Euro sermaye gerektirdiğini ve Gmbh'nin yatırımcı vizesi için en uygun şirket tipi olduğunu belirtmektedir.","Ayrıca, iş planı hazırlamanın önemi, şirketin aktif olması gerekliliği ve yüksek sermaye olmadan önce şirket kurmanın ve ileride taşınma opsiyonu oluşturmanın mantıklı olabileceği gibi gerçekçi bilgiler de paylaşılmaktadır. Video, şirket kurma sürecinin sadece para ile değil, iş planıyla da uyumlu olması gerektiğini vurgulamaktadır."]},"endTime":972,"title":"Almanya'da Şirket Kurma ve Yatırımcı Vizesi Rehberi","beginTime":0}],"fullResult":[{"index":0,"title":"Almanya'da Şirket Kurma Soruları","list":{"type":"unordered","items":["Almanya'da şirket kurma, oturum alma ve maliyetlerle ilgili sorular uzun süredir sorulmaktadır.","Video, bu sorulara kısa ve net cevaplar vermek amacıyla doğa yürüyüşü yaparken çekilmektedir.","En çok sorulan sorular arasında \"Almanya'da nasıl şirket kurabilirim?\" ve \"Şirket kurarak oturum alabilir miyim?\" yer almaktadır."]},"beginTime":0,"endTime":86,"href":"/video/preview/17632503169353800360?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=0&ask_summarization=1"},{"index":1,"title":"Almanya'da Şirket Kurma ve Yatırımcı Vizesi","list":{"type":"unordered","items":["Almanya'da şirket kurmak ve yatırımcı vizesi almak iki ayrı konudur.","Almanya'da şirket kurmak herkes için mümkündür, almanca bilme veya Almanya'ya gelme gereği yoktur.","Şirket kurulduktan sonra yatırımcı vizesi almak isteyen kişi, şirket üzerinden oturum talebinde bulunabilir."]},"beginTime":86,"endTime":128,"href":"/video/preview/17632503169353800360?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=86&ask_summarization=1"},{"index":2,"title":"Almanya'da Şirket Türleri","list":{"type":"unordered","items":["Almanya'da farklı şirket türleri bulunmaktadır: UG (sermayesiz kurulan şirketler), GmbH (limited şirketi), AG (anonim şirketler) ve ortaklık formatları.","Yatırımcı vizesi almaya uygun olan şirket tipi GmbH (limited şirketi)dir.","Bu şirketi açmak için 25.000 Euro'luk sermaye gerekmekte, yarısını yatırarak 12.500 Euro ile de teknik olarak şirket açmak 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gidip gelebilirsiniz.","Yatırımcı vizesi başvurusunda şirketin büyüklüğü, yapacağı iş ve giderleri belirleyicidir.","Yazılımcı veya danışmanlık gibi düşük giderli işler için minimum 50.000-100.000 Euro arası sermaye gerekmektedir."]},"beginTime":256,"endTime":407,"href":"/video/preview/17632503169353800360?parent-reqid=1776537900231177-8736944808574758150-balancer-l7leveler-kubr-yp-sas-31-BAL&text=Yanit+Group&t=256&ask_summarization=1"},{"index":5,"title":"Yatırımcı Vizesi Koşulları","list":{"type":"unordered","items":["Şirketin kurulduğu bölgedeki bölgesel ihtiyacı karşılama ve bazı durumlarda istihdam sağlama gereklidir.","Ticaret odalarının görüşleri önemli olup, tüm koşullar sağlandığında maksimum üç yıllık, genelde birer birer yıl olarak çalışma ve oturma izni verilir.","Üçüncü yıl sonunda şirket ayaktaysa ve diğer koşullar sağlanırsa sınırsız oturma izni 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