The curve C C\,C has equation y=a(x+b)2+cy=a(x+b)^2+cy=a(x+b)2+c and minimum point (3,8)(3,8)(3,8). The curve is translated by the vector (−40)\begin{pmatrix}-4\\0\end{pmatrix}(−40) and the translated curve passes through (−6,13)(-6,13)(−6,13).
State the values of b b\,b and ccc.
Find aaa.