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June 18th, 2012, 12:43 AM  #1 
Senior Member Joined: Apr 2008 Posts: 193 Thanks: 3  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 xintercepts 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. 
June 18th, 2012, 12:54 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,209 Thanks: 517 Math Focus: Calculus/ODEs  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: 
June 18th, 2012, 04:55 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond  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 ² =  1 + b ² b²  6b + 9 = b² + 2b + 1 6b + 9 = 2b + 1 8b = 8 b = 1. 

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