SOLUTION: 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 ?

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Question 1203022: 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 ?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
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.




Edwin
Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


What is the meaning of the "b" in the statement "|B - A|= 12 b"?

If we ignore the "b", then the response from the other tutor is as much as we can do with the problem.

If the "b" has some meaning, then the problem might have a unique solution -- IF you tell us what "b" is....

Re-post if necessary.
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