I've been trying to figure out how to do the last part of this question for a long time but I still can't..
Can someone please help me..
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
For a) I got ( b/a , c - b^2/a )
For b) I got c= (b^2+b) /a
Any help would be greatly appreciated...