Find a second-degree polynomial P such that P(1) = 5, P'(1) = 4, and P''(1) = 8.

P(x)= ?

P(x) = ax^2 + bx + c P'(x) = 2ax + b P''(x) = 2a

P''(1) = 8, then 2a=8 , a=4

P'(1) = 4, then 2*4*1+b=4, b=4-8=-4

P(1) = 5, then 4*1^2+(-4)*1+c=5, c=5

so P(x) = 4x^2 -4x + 5

answer is P(x) = 4x^2 -4x + 5

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