[tex]f(x)=2x^{2} +4x+c\\
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A=(1,2)~~\land~~A\in f(x)\\
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2\cdot 1^{2} +4\cdot 1+c=2\\
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2+4+c=2\\
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6+c=2\\
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c=2-6\\
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c=-4\\
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f(x)=2x^{2} +4x-4\\
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a=2~~\Rightarrow ~~a>0~~\Rightarrow ~~ramiona~~paraboli~~skierowane~~do ~~gory\\\\
Obliczam~~wierzcholek~~paraboli:\\
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W=(p,q)\\
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[/tex]
[tex]p=\dfrac{-b}{2a} ~~\land~~q=\dfrac{-\Delta }{4a} \\
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a=2,~~b=4,~~c=-4\\
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\Delta =b^{2} -4ac\\
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\Delta = 4^{2} -4\cdot 2 \cdot (-4)=16+32=48\\
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p=\dfrac{-4}{4} =-1\\
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q=\dfrac{-48}{8} =-6\\
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W=(-1,-6)\\
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Gdy:\\
a>0~~(ramiona~~paraboli~~skierowane~~do~~gory)~~\land ~~W=(p,q)~~\Rightarrow ~~Z_{w} =(q, + \infty )\\
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a=2~~~~(a>0)~~\land ~~W=(-1,-6)~~\Rightarrow ~~Z_{w} =<-6,+ \infty )\\
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Odp:~~c=-4~~a ~~zbior~~wartosci~~funkcji~~kwadratowej~~f(x)~~wynosi~~Z_{w} =<-6,+ \infty ).[/tex]
