Find the coefﬁcients $a, b, c$ and $d$ so that the curve shown in the accompanying ﬁgure is the graph of the equation. 
Find the coefﬁcients $a, b, c$ and $d$ so that the curve shown in the accompanying ﬁgure is the graph of the equation $y = ax^3 + bx^2 + cx + d$. 
I have no clue how to solve this. This looks like nothing from any example in my book. How do I solve this? Where do I even start?

$\begin{vmatrix}
x^3&x^2&x&1&y\\
0^3&0^2&0&1&10\\
1^3&1^2&1&1&7\\
3^3&3^2&3&1&-11\\
4^3&4^2&4&1&-14\\
\end{vmatrix}=
\begin{vmatrix}
x^3&x^2&x&1&y\\
0&0&0&1&10\\
1&1&1&1&7\\
27&9&3&1&-11\\
64&16&4&1&-14\\
\end{vmatrix}=
-72x^3+432x^2-144x-720+72y=
x^3-6x^2+2x+10-y=0$
