Stumped on a quadratic question

[Winston]

Can anyone help with this one? I've got most of it, but just can't work out iii)
Thanks heaps

Two quadratic graphs both pass through the point (1,4)

One Graph has the equation: y=x^2+bx+c
and the other has the equation: y=-x^2+dx+e

i) Find the values of b, c, d and e if both graphs also pass through the origin.

ii) Show that if both graphs have one other point in common (not necessarily the origin), then the x-coordinate of the point in common is given by:   x=(d-b-2)/2

iii) Show that if both graphs have NO other point in common then: d=b+4
     and find an expression for e in terms of c.


That's it, word for word. It's doing my head in. I thought I knew quadratics really well   

[TrueTears]

[1] and [2]

We know it passes through

subbing this point in [1] and [2] yields

and

solving for c and e respectively yields:

and

subbing this back into [1] and [2] yields:

and

now solving the simultaneous equation yields:



rearranging leads to :

now for x to only have ONE solution we require

so

expanding leads to

solving for b yields (subbing all the values into the general quadratic formula will yield this result)

solving for d yields as required

[Winston]

Awesome. THanks man!