Question

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

a =
b =
c =

Answer 1

if p(2) = 6, substituting in the p(x) function, 6 = 4a + 2b + c

p ' (x) = 2ax + b, therefore if p ' (2) = 2, this means that 2 = 4a + b

p '' (x) = 2ax + b, therefore if p '' (2) = 3, this means that 3 = 2a and a = 3/2

substituting 3/2 for a in 2 = 4a + b gives a solution for b = -4

substituting for a and b in the first equation, 6 = 4(3/2) + 2(-4) + c gives a solution that c = 8