Can you please help me with the last part of this question...(Speechless)(Speechless)

the equation of a curve is y=ax^2 - 2bx +c where a,b and c are constants with a>0 .

a) Find in terms of a,b and c the coordinates of the vertex of the curve

b) Given that the vertex of the curve lies on the line y=x , find an expression for c in terms of a and b.

Show that in this case, whatever the value of b, c is greater than or equal to -1/4a