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#1 2007-11-07 23:16:45
- EPhillips1989
- Member
- Registered: 2007-11-03
- Posts: 29
Functions
can anyone help me with this question
describe all functions f(x)=ax^2+bx+c
such that f(1)=2 and f(-1)=6
i dont really know what this question is asking for please help!!!!
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#2 2007-11-07 23:47:22
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Functions
It wants you to find constraints on a, b and c such that the 2 conditions are always met.
So, f(1) = a+b+c = 2, by the first condition.
By the second, f(-1) = a-b+c = 6.
Subtracting the second equation from the first gives that 2b = -4, and hence b = -2.
Substituting that into either of the first 2 equations tells you that a+c=4, and that's all we can deduce.
So, the general form of the equation that fits those conditions would be tx² - 2x + (4-t), where t is some real number.
Why did the vector cross the road?
It wanted to be normal.
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