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>-1/4a or c=-1/4a.
So the vertex is on (b/a, c-b^2/a) and c=b(b+1)/a. Any ideas about the last part?
(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>-1/4a or c=-1/4a.
So the vertex is on (b/a, c-b^2/a) and c=b(b+1)/a. Any ideas about the last part?