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

 Jun 17, 2021
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Let f(x) = ax2 + bx + c

⇒f(0) = c = 3

f(1) = a + b + c = -5

           ⇒ a + b = -8          

f(2) = 4a + 2b + c = 7 

           ⇒ 4a + 2b = 4   ⇒ 2a + b = 2

⇒ 2a + b - a - b = 2 + 8 

       a = 10

       b = -18

 

f(x) = 10x2 - 18x + 3

 Jun 17, 2021

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