Matematică
gabrielutzzama
4

1)Sa se determine functiile de gradul 2 f:R->R,stiind ca: a)f(0)=1;f(1)=3;f(2)=7 b)f(-1)=1;f(2)=7;f(-2)=3

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(1) Răspunsuri
adhcbfgv

a. f(x)=ax²+bx+c f(0)=1, c=1 f(1)=3, a+b+1=3, a+b=2 f(2)=7, 4a+2b+1=7, 4a+2b=6, 2a+b=3, a+a+b=3, a+2=3, a=1, b=2-a=1 f(x)=x²+2x+1 b. f(-1)=a-b+c=1 f(2)=4a+2b+c=7 f(-2)=4a-2b+c=3 adunam ultimele doua relatii 8a+2c=10 4a+c=5, c=5-4a inlocuim in primele doua a-b+5-4a=1, -3a-b=-4 4a+2b+5-4a=7, 2b=2, b=1 -3a-1=-4, -3a=-3, a=1 c=5-4a=1 f(x)=x²+x+1

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