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Find the quadratic polynomial f(x) such that f(0) = 3, f(1) = -5, and f(2) = 7.

 May 22, 2022
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Use the quadratic form in this case, which is ax^2 + bx + c. ( = 3, = -5, = 7)

Substituting in 0 gives us c = 3. Keep substituting for x and for c. If you do this for the rest, you'll end up having sets of equations

which comes out as

a + b = -8

4a+2b = 4

I recommend using the addition method but you can do whatever method you like for this. I chose to multiply both sides of the first equation by -4 , and I got 

-2b=36 and b=-18. I think you know where this is going.                          

 May 22, 2022

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