Can you show us your working out? We can get a better idea of if the answer is right and if not what is going wrong.
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...
We know the vertex of the parabola and the y intercept and since a is greater than zero so c has to be greater than c - (b^2)/a
and c= (b^2 +b) /a
so (b^2 +b) /a >c - (b^2)/a
(2b^2 + b )/a > c
but that doesn't look anything like what they want ..
And I don't know what else I could do
Any hint that might help me?