A. TANIM
\n a \u00b9 0 ve a, b, c \u00ce IR olmak \u00fczere, f : IR \u00ae IR tan\u0131mlanan f(x) = ax2 + bx + c bi\u00e7imindeki fonksiyonlara ikinci dereceden bir de\u011fi\u015fkenli fonksiyonlar denir.
\n\u0130kinci dereceden fonksiyonun analitik d\u00fczlemdeki g\u00f6r\u00fcnt\u00fcs\u00fcne parabol denir.
\nParabol, d\u00fczg\u00fcn tel par\u00e7a-s\u0131n\u0131n u\u00e7lar\u0131ndan tutularak b\u00fck\u00fclmesiyle olu\u015fan, yandaki gibi kollar\u0131 yukar\u0131ya do\u011fru ya da a\u015fa\u011f\u0131ya do\u011fru olan bir e\u011fridir.<\/p>\n
B. PARABOL\u00dcN TEPE NOKTASI
\n1) f(x) = ax2 + bx + c fonksiyonunun tepe noktas\u0131<\/p>\n
T(r, k) olmak \u00fczere,<\/p>\n
\u00dc Parabol do\u011frusuna g\u00f6re simetriktir.<\/p>\n
do\u011frusu parabol\u00fcn simetri eksenidir.<\/p>\n
y = a(x \u2013 r)2 + k fonksiyonunun grafi\u011finin tepe noktas\u0131 T(r, k) d\u0131r.C. GRAF\u0130\u011e\u0130N EKSENLER\u0130 KEST\u0130\u011e\u0130 NOKTALAR
\nParabol\u00fcn Ox eksenini kesti\u011fi noktalar A ve B, Oy eksenini kesti\u011fi nokta C olsun.
\nax2 + bx + c = 0 \u0131n k\u00f6kleri x1 ve x2 ise A(x1, 0), B(x2, 0), C(0, c) dir.<\/p>\n
\u00dc ax2 + bx + c = 0 denkleminde
\nD = b2 \u2013 4ac > 0 ise, parabol Ox eksenini farkl\u0131 iki noktada keser.
\nD = b2 \u2013 4ac < 0 ise, parabol Ox eksenini kesmez.\nD = b2 \u2013 4ac = 0 ise, parabol Ox eksenine te\u011fettir.\nD. x2 N\u0130N KATSAYISI OLAN a NIN \u0130\u015eARET\u0130\n1)a>0 ise parabol\u00fcn kollar\u0131 yukar\u0131 do\u011fru olup,f(x),in en k\u00fc\u00e7\u00fck de\u011feri tepe noktas\u0131n\u0131n ortinat\u0131 olan k d\u0131r.2) a < 0 ise, parabol\u00fcn kollar\u0131 a\u015fa\u011f\u0131 do\u011fru olup, f(x) in en b\u00fcy\u00fck de\u011feri tepe noktas\u0131-n\u0131n ordinat\u0131 olan k d\u0131r.\n.a>0 ise parabol\u00fcn kollar\u0131 a\u015fa\u011f\u0131 do\u011fru olup f(fx) in en b\u00fcy\u00fck de\u011feri tepe noktas\u0131n\u0131n ortinat\u0131 olan k d\u0131r.3) |a| b\u00fcy\u00fcd\u00fck\u00e7e kollar daral\u0131r. Buna g\u00f6re, yandaki parabollere g\u00f6re, f deki x2 nin katsay\u0131s\u0131, g deki x2 nin katsay\u0131s\u0131ndan b\u00fcy\u00fckt\u00fcr.
\n|a| b\u00fcy\u00fcd\u00fck\u00e7e kollar daral\u0131r. Buna g\u00f6re , yandaki parabollere g\u00f6re ,f deki x2 nin katsay\u0131s\u0131 g deki x2 nin katsay\u0131s\u0131ndan b\u00fcy\u00fckt\u00fcrf(x) = ax2 + bx + c fonksiyonunun grafi\u011fini \u00e7izmek i\u00e7in,
\n1) Fonksiyonun tepe noktas\u0131 bulunur.
\n2) Fonksiyonun eksenleri kesti\u011fi noktalar bulunur.
\n3) a n\u0131n i\u015faretine bak\u0131larak parabol\u00fcn kollar\u0131n\u0131n y\u00f6n\u00fc belirlenir.
\nE. GRAF\u0130\u011e\u0130 VER\u0130LEN PARABOL\u00dcN DENKLEM\u0130N\u0130N YAZILMASI
\n1. Parabol\u00fcn Ox Eksenini Kesti\u011fi Noktalar Biliniyorsa<\/p>\n
y = f(x) = a(x \u2013 x1) (x \u2013 x2) … (1) dir.
\n Burada a de\u011ferini bulmak i\u00e7in, parabol \u00fczerindeki herhangi bir noktan\u0131n de\u011ferleri (1) de yaz\u0131l\u0131r.
\n2. Parabol\u00fcn Tepe Noktas\u0131 Biliniyorsa<\/p>\n
y = f(x) = a(x \u2013 r)2 + k … (1) dir.
\n Burada a de\u011ferini bulmak i\u00e7in, parabol \u00fczerindeki herhangi bir noktan\u0131n de\u011ferleri (1) de yaz\u0131l\u0131r.
\n3. Parabol\u00fcn Ge\u00e7ti\u011fi \u00dc\u00e7 Nokta Biliniyorsa<\/p>\n
y1 = ax12 + bx1 + c … (1)
\n y2 = ax22 + bx2 + c … (2)
\n y3 = ax32 + bx3 + c … (3)
\n Bu \u00fc\u00e7 denklemi ortak \u00e7\u00f6zerek a, b, c yi buluruz.
\nF. PARABOL \u0130LE DO\u011eRUNUN D\u00dcZLEMDEK\u0130 DURUMU<\/p>\n
y = f(x) = ax2 + bx + c parabol\u00fc ile y = g(x) = mx + n do\u011frusunu ortak \u00e7\u00f6zelim.
\nf(x) = g(x)
\nax2 + bx + c = mx + n<\/p>\n
ax2 + (b \u2013 m)x + c \u2013 n = 0 … (*)<\/p>\n
(*) denkleminin k\u00f6kleri (varsa) do\u011fru ile parabol\u00fcn kesi\u015fti\u011fi noktalar\u0131n apsisleridir.
\n Buna g\u00f6re, (*) denkleminde;
\nD > 0 ise, parabol do\u011fruyu farkl\u0131 iki noktada keser.
\nD< 0 ise, parabol ile do\u011fru kesi\u015fmez.\nD = 0 ise, parabol do\u011fruya te\u011fettir.\n\u00dc y = ax2 + bx + c parabol\u00fc ile y = dx2 + ex + f parabol\u00fcn\u00fcn d\u00fczlemdeki durumu incelenirken yukar\u0131dakine benzer bi\u00e7imde i\u015flemler yap\u0131l\u0131r.\n<\/p>\n","protected":false},"excerpt":{"rendered":"
A. TANIM a \u00b9 0 ve a, b, c \u00ce IR olmak \u00fczere, f : IR \u00ae IR tan\u0131mlanan f(x) = ax2 + bx + c bi\u00e7imindeki fonksiyonlara ikinci dereceden bir de\u011fi\u015fkenli fonksiyonlar denir. \u0130kinci dereceden fonksiyonun analitik d\u00fczlemdeki g\u00f6r\u00fcnt\u00fcs\u00fcne parabol denir. Parabol, d\u00fczg\u00fcn tel par\u00e7a-s\u0131n\u0131n u\u00e7lar\u0131ndan tutularak b\u00fck\u00fclmesiyle olu\u015fan, yandaki gibi kollar\u0131 yukar\u0131ya do\u011fru …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7349,7348,7347],"class_list":["post-3132","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-analitik-duzlem","tag-fonksiyon","tag-parabol"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3132","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3132"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3132\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}