Find the values of a , b , and c in the quadratic function p(x)=ax^2+bx+c such that p(2)=7, p′(2)=4, and p′′(2)=3.

Answer 1

p' = 2ax + b
p" = 2a
so, 2a = 3
a = 3/2

p' = 3x+b
p'(2) = 4, so 12+b = 4; b = -8

p = 3/2 x^2 - 8x + c
p(2) = 7, so 6-16+c = 4; c = 16

p(x) = 3/2 x^2 - 8x + 16

Answer 2

oops. catch my typo (in p'(2))