Page 196 - Demo

190VargjetAFT%u00cbSI9.2 Vargjet kuadratikeVargjet kuadratike mund t%u00eb p%u00ebrftohen dhe shprehen duke p%u00ebrdorur: rregull%u00ebn kufiz%u00eb pas kufize;rregull%u00ebn vend-kufiz%u00eb.Vargjet kuadratike jan%u00eb vargje n%u00eb t%u00eb cilat:ndryshesat e radh%u00ebs s%u00eb dyt%u00eb nd%u00ebrmjet kufizave jan%u00eb konstante;fuqia m%u00eb e madhe e n n%u00eb kufiz%u00ebn e n-t%u00eb, %u00ebsht%u00eb 2.koeficienti i n2 %u00ebsht%u00eb sa gjysma e konstantes s%u00eb ndryshes%u00ebs s%u00eb dyt%u00eb.SHEMBULLGjeni pes%u00eb kufizat e para t%u00eb vargut, duke p%u00ebrdorur rregull%u00ebn kufiz%u00eb pas kufize.Kufiza e par%u00eb: 5 Rregulla: Shto numrat tek t%u00eb nj%u00ebpasnj%u00ebsh%u00ebm. p g5, 6, 9, 14,+1 +3 +5 +721SHEMBULLKufiza e n-t%u00eb e vargut %u00ebsht%u00eb n2 + n + 1a Gjeni pes%u00eb kufizat e para t%u00eb vargut. b Kontrolloni n%u00ebse vargu %u00ebsht%u00eb varg kuadratik.a 3, 7, 13, 21, 31, %u2026 T(1) = 12 + 1 + 1 = 3T(2) = 22 + 2 + 1 = 7T(3) = 32 + 3 + 1 = 13T(4) = 42 + 4 + 1 = 21T(5) = 52 + 5 + 1 = 31b 3, 7, 13, 21, 31, %u20264 6 8 102 22Meq%u00eb ndryshesa e radh%u00ebs s%u00eb dyt%u00eb %u00ebsht%u00eb konstante, at%u00ebher%u00eb vargu %u00ebsht%u00eb kuadratik.T(1) %u00ebsht%u00eb kufiza e par%u00eb e vargut.T(2) %u00ebsht%u00eb kufiza e dyt%u00eb e vargut. P%u00ebr vargun 2, 5, 10, 17, 26, ... %u201cshtoji %u00e7do kufize numrin tek t%u00eb radh%u00ebs, duke filluar me 3-shin%u201d. Kufiza e n-t%u00eb = n2 + 11 2 6 3 4 5 7T(n )nV P%u00ebr nj%u00eb varg kuadratik, n%u00eb qoft%u00eb se do t%u00eb vizatoni grafikun T(n) n%u00eb lidhje me n, do t%u00eb merrni nj%u00eb bashk%u00ebsi pikash t%u00eb vendosura sipas nj%u00eb parabole. SHEMBULLGjeni kufiz%u00ebn e n-t%u00eb t%u00eb vargjeve kuadratike t%u00eb m%u00ebposhtme.a 3, 8, 15, 24, 35, %u2026 b 5, 11, 21, 35, 53, %u2026a 3, 8, 15, 24, 35, %u2026 +5 +7 +9 + 11 +2 +2 +2Kufiza e n-t%u00eb =n2 %u00b1 %u25a1Krahasoni vargun me kufizat e para t%u00eb vargut n2. 3, 8, 15, 24, 35%u2013n2 1, 4, 9, 16, 25 2, 4, 6, 8, 10Nga krahasimi, v%u00ebm%u00eb re se:Vargu linear, kufiza e n-t%u00eb = 2nVargu kuadratik, kufiza e n-t%u00eb = n2 + 2nb 5, 11, 21, 35, 53, %u2026+6 +10 +14 +18+4 +4 +4Kufiza e n-t%u00eb = 2n2 %u00b1 %u25a1Krahasoni vargun me kufizat e para t%u00eb vargut 2n2. 5, 11, 21, 35, 53%u20132n2 2, 8, 18, 32, 50 3, 3, 3, 3, 3 Ndryshesa konstante: +3Vargu kuadratik, kufiza e n-t%u00eb = 2n2 + 3Koeficienti i n2 %u00ebsht%u00eb sa gjysma e ndryshes%u00ebs s%u00eb radh%u00ebs s%u00eb dyt%u00eb.Vargje kuadratike jan%u00eb vargjet ku T(n) jepet nga nj%u00eb shprehje kuadratike (trinom i fuqis%u00eb s%u00eb dyt%u00eb), me ndryshore n.Ndryshesa e radh%u00eb s%u00eb par%u00ebNdryshesa e radh%u00ebs s%u00eb dyt%u00ebNdryshesa e radh%u00ebs s%u00eb par%u00eb.Ndryshesa e radh%u00ebs s%u00eb dyt%u00eb.Ndryshesa e radh%u00ebs s%u00eb par%u00eb.Ndryshesa e radh%u00ebs s%u00eb dyt%u00eb.