Matematyka
kamilaa9
2017-06-24 10:17:44
Zadana w załączniku Proszę bardzo o rozwiązanie Funkcja kwadratowa
Odpowiedź
kamilak8
2017-06-24 16:55:12

[latex]1.\ZW = extless 3,infty)\ZW = (q,infty)\q = 3\q = frac{-Delta}{4a}\\A)\f(x) = frac{1}{2}x^{2}-2x+5\\Delta = b^{2}-4ac=(-2)^{2}-4cdotfrac{1}{2}cdot5 = 4-2cdot 5 = 4-10 = -6\\q = frac{-(-6)}{4cdotfrac{1}{2}}=frac{6}{2} = 3[/latex] [latex]B)\f(x) = frac{1}{2}x^{2}-2x+6\\Delta = (-2)^{2}-4cdotfrac{1}{2}cdot 6 = 4 - 12 = -8\\q = frac{-(-8)}{4cdotfrac{1}{2}}} = frac{8}{2} = 4 eq 3[/latex] [latex]C)\f(x) = frac{1}{2}x^{2}-2x+7\\Delta = (-2)^{2}-4cdotfrac{1}{2}cdot7 = 4 - 14 = -10\\q = frac{-(-10)}{4cdotfrac{1}{2}}=frac{10}{2} = 5 eq 3[/latex] [latex]D)\f(x) = frac{1}{2}x^{2}+2x+7 \\Delta = 2^{2}-4cdotfrac{1}{2}cdot7 = 4 - 14 = -10\\q = frac{-(-10)}{4cdotfrac{1}{2}} = frac{10}{2} = 5 eq 3\\Odp. A.[/latex] [latex]2.\f(x) = 2x^{2}-x-3\\a = 2, b = -1, c = -3\\W = (p,q)\\p = frac{-b}{2a} = frac{-(-1)}{2cdot2}=frac{1}{4}\\q = frac{-Delta}{4a}=frac{-((1-4cdot2cdot(-3))}{4cdot2}=frac{-(1+24)}{8}=-frac{25}{8}\\W = (frac{1}{4};-frac{25}{8})\\Odp. C.[/latex] [latex]3.\f(x) = -2x^{2}+6x-5\\x = p = frac{-b}{2a} = frac{-6}{2cdot(-2)}=frac{-6}{-4} = frac{3}{2}[/latex] [latex]A)\f(x) = -2x^{2}-5\a = -2, b = 0, c = -5\\x = p = frac{-b}{2a} = frac{0}{-4} = 0 eq frac{3}{2}[/latex] [latex]B)\f(x) = x^{2}+3x-1\\x = p = frac{-b}{2a} = frac{-3}{2cdot1} = -frac{3}{2} eq frac{3}{2}[/latex] [latex]C)\f(x) = frac{1}{2}x^{2}-frac{3}{2}x\\x = p = frac{-b}{2a} = frac{-(-frac{3}{2})}{2cdotfrac{1}{2}}=frac{3}{2}[/latex] [latex]D)\f(x) = -6x^{2}+2x-5\\x = p = frac{-b}{2a} = frac{-2}{2cdot(-6)}}=frac{1}{6} eq frac{3}{2}[/latex] [latex]Odp. C.[/latex]

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