Interpolation problem

[SGS]

Ok so in school I have just recently begun doing interpolation. I am having a problem deriving a 2nd order polynomial when I am given two points and a evaluated derivative. For instance, given q(0)=-1, q(1)=-1, and q'(1)=4. I know how to do it when I have 3 points, but the q' presents me with a problem I am struggling with. Any help is appreciated thanks in advance.

SGS

[BruceZ]

[ QUOTE ]
Ok so in school I have just recently begun doing interpolation. I am having a problem deriving a 2nd order polynomial when I am given two points and a evaluated derivative. For instance, given q(0)=-1, q(1)=-1, and q'(1)=4. I know how to do it when I have 3 points, but the q' presents me with a problem I am struggling with. Any help is appreciated thanks in advance.

SGS

[/ QUOTE ]

q(x) = Ax^2 + Bx + C
q'(x) = 2Ax + B

q(0) = C = -1
q(1) = A + B + C = -1
q'(1) = 2A + B = 4

subtracting q(1) from q'(1) gives

A - C = 5
A - (-1) = 5
A = 4 => B = -4

q(x) = 4x^2 - 4x - 1