Find a second degree polynomial p(x) such that p(2) = 1, p'(2) = -2, and p''(2) = 3.  

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A second degree polynomial p(x) has to be determined such that p(2) = 1, p'(2) = -2, and p''(2) = 3

Let p(x) = ax^2 + bx + c

p(2) = a*4 + b*2 + c = 1

p'(2) = 2a*2 + b = -2

p''(2) = 2a = 3

=> a = 3/2

6 + b = -2

=> b = -8

6 - 16 + c = 1

=> c = 11

The polynomial p(x) = (3/2)*x^2 - 8x + 11

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