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If f(0) = 0, f(1) = 1, f(2) = 5 ,  and ax^2+bx+c=0, what is the value of f(3)?

 Dec 18, 2020
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f(0)  = a (0^2) + b(0) + c  = 0      shows that c =0

 

f(1) = a(1^2) + b(1) =1      so      a + b = 1 

f(2)  = a(2^2) + b(2) = 5    so    4a + 2b = 5

                                               solving these two equations results in a = 3/2   b = - 1/2

 

f(x)  = 3/2  x^2    -1/2 x 

f(3) = 3/2 (3^2)  - 1/2 (3) = 12

 Dec 18, 2020

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