Question 1203022
<pre>
1) if roots of a equation :f(x) = a(x-2)² + k,  a ≠ 0, are A  and B, |B - A|= 12 b, find value of k ?

There's no way to find a value for k.

f(x) is a parabola with vertex (2,k).  So its axis of symmetry is the vertical
line x = 2.  Its roots are A and B, so its x-intercepts are (A,0) and (B,0).
Since |B - A| = 12, they are 12 units apart, so each is 6 units from the axis of
symmetry, so they are (-4,0) and (8,0)

So any parabola like this would do, this has vertex at (2,-12), so k = -12.
There are infinitely many possibilities.  There is not enough information to
find k.


{{{drawing(400,400,-7,11,-14,4, green(line(2,-16,2,7)),graph(400,400,-7,11,-14,4,(1/3)(x-2)^2-12))}}}

Edwin</pre>