hi Deon588,

Have you got a, b and c yet?

I'll assume yes.

That fixes the parabola (ie. there's only one answer) and the line is obviously unique. 
But B can move about on the parabola and so that means M moves too.

I'd call M (x,0) and write the coordinates of B and A in terms of this.

Then you write an expression for BA in terms of x, differentiate, and hence get the maximum.

I'd better go and get a piece of paper and try it out.

Bob

hi Deon588

I got a = -2    b = -4    and c = 0

Then for the points:

So

So you need

Can you take over from here?

Bob

Last edited by bob bundy (2011-09-29 11:07:23)

hi Deon588

d(BA)/dx is a special notation used in the differential calculus.

It gives you a way of finding the maximum value of an expression (amongst many, many uses!).

It's too big a topic to start in answer to the question, if you haven't met it before.

But don't worry.  As the expression

is a quadratic there's another way to get the maximum value.

I've put the graph below.  As you can see it does have a maximum value.  Would you be able to work out the x, at this point?

Bob

Last edited by bob bundy (2011-09-29 17:53:04)

Hi Deon588;

Yes, there is a way using just algebra.

Thanks a lot Bob and Bobbym.  I have done this many times before but the way the question was written confused me a bit