Find a quadratic polynomial, P(x), such that p(0) = 1, P(1) = 5, P(2) = 11

General quadratic polynomial:  P(x) = ax^2 + bx + c

 

P(0) = 1   ⇒   1 =  c

 

P(1) = 5   ⇒   5 = a + b + c               so 5 = a + b + 1            or   4 = a + b   (1)

 

P(2) = 11  ⇒  11 = 4a + 2b + c          so 11 = 4a + 2b + 1      or  10 = 4a + 2b  (2)

 

Multiply (1) by 2 and subtract from from (2) to get:    2 = 2a  or a = 1

 

Put this back into (1) to get:  4 = 1 + b  or b = 3

 

So:  P(x) = x^2 + 3x + 1

 

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