Classify the degenerate point; 
Given $$f(x,y)=y^4+y(x-1)^2-8y^2$$
  Find the three critical points, use Hessian method to classify the two non degenerate points.  

Then: By considering the value of $f$ along the curve $y=c(x-1)^2$ for different values of $c$ , classify the degenerate critical point.  
Now, I have found the three critical points being $$(x,y)=(1,0),(1,-2),(1,2)$$
And using the hessian method, I have found that $(1,-2),(1,2)$  are  non-degenerate saddle points. 
But I am confused on how I should be using the function $f=c(x-1)^2$ to classify $(1,0)$ .

Substitute: $y=c(x−1)^2$ into $f(x,y)$ 
find $fxx$
Substitute values of your degenerate point
Note: $fxx>0 =>minimum$, $fxx<0 =>maximum$
