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June 17th, 2012, 11:43 PM   #1
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Is the answer key wrong?

This is the question.

Consider an absolute value equation in the form f(x) = a + I x + b I. Its graph has the vertex at (-1,-2) and the x-intercepts at (-3,0) and (1,0). Find the values of a and b.

This is actually a very easy question. My answer is a=-2 and b=-1.

But, the answer key says a=-2 and b=1.

I don't know if my answer or the answer key is wrong.

Could someone please explain? Thanks.
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June 17th, 2012, 11:54 PM   #2
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Re: Is the answer key wrong?

For the function:



The vertex is at

Putting the given function into this form, we have:



Hence the vertex is:

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June 18th, 2012, 03:55 AM   #3
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Re: Is the answer key wrong?

| -3 + b | + a = 0 [1]
| 1 + b | + a = 0 [2]

[1] - [2]: | -3 + b | - | 1 + b | = 0
| -3 + b | = | 1 + b |
| -3 + b | = | 1 + b |
b - 6b + 9 = b + 2b + 1
-6b + 9 = 2b + 1
8b = 8
b = 1.
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