Find the values of a , b , and c in the quadratic function p(x)=ax2+bx+c such that p(2)=6, p'(2)=2, p"(2)=3

Answer 1

p(2) = 4a + 2b + c = 6
p'(x) = 2ax + b
p'(2) = 4a + b = 2 ---> b = 2 - 4a
b = 1 - 2a

p''(x) = 2a = 3
a = 3/2
b = 2 - 4(3/2) = -4

in 1st equation:
4(3/2) - 8 + c = 6
c = 8