TITLE: Find the values of a cubical function graph
QUESTION [1 upvotes]: I'm having some problem with this question,
I could only find the value of [1-5] and [1-7], which is quite easy.
But in the others I'm having some difficulty.
Thanks in advance.

REPLY [0 votes]: You can use Lagrange interpolation :
The Idea : If you know n+1 values at respectively n+1 disctinct  points for a polynom of degree n , so you know the polynom completely. (Because of number of coefficient of polynom (argument of dimension)).
So for your points $ P(a_i) $ for i from 0 to 3 ,
Lagrange said : 
$$ P(X)=\sum_{i=0}^3P(a_i) \prod_{j=0,j \neq i}^3\dfrac{(X-a_j)}{a_i-a_j} $$
Develop and win.
2) You can also solve your 4x4 system given by plugin values  in the equation.
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