Hello & welcome
The points A, B, C are on the curve.
Therefore, , because at the point A, when the absciss is 17, the ordinate is 3.
This goes the same way for B & C : and
Substitute in the expression of
These three equations will give you relations between a,b,c, and z.
Now, there is one more information : there is a local minimum at the point C.
This means that at the point C, the derivative is equal to 0.
This will give you a relation between a and b.
So now it's OK, you have 4 equations with 4 unknown variable... Try to get out from this
If you don't understand, just ask...