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Rewrite the expression 6j^2 - 4j + 12 in the form c(j + p)^2 + q, where c, p, and q are constants. What is q/p?

 

Quick help would be really appreciated 

 Oct 23, 2017

Best Answer 

 #1
avatar+7352 
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6j2 - 4j + 12       Factor out a  6 .

 

=  6(j2 - 2/3j + 2)       Add and subtract  (2/6)2

 

=  6(  j2 - 2/3j + (2/6)2 + 2 - (2/6)2  )      Factor  j2 - 2/3j + (2/6)2  as a perfect square trinomial.

 

=  6(  (j - 2/6)2 + 2 - 4/36  )        Combine  2  and  -4/36 .

 

=  6(  (j - 1/3)2 +  17/9 )             Distribute the  6 .

 

=  6(j - 1/3)2 + 34/3

 

Now it is in the form  c(j + p)2 + q  ,  and  q = 34/3  and  p = -1/3  →  q/p  =  (34/3) / (-1/3)  =  -34

 Oct 23, 2017
 #1
avatar+7352 
+1
Best Answer

6j2 - 4j + 12       Factor out a  6 .

 

=  6(j2 - 2/3j + 2)       Add and subtract  (2/6)2

 

=  6(  j2 - 2/3j + (2/6)2 + 2 - (2/6)2  )      Factor  j2 - 2/3j + (2/6)2  as a perfect square trinomial.

 

=  6(  (j - 2/6)2 + 2 - 4/36  )        Combine  2  and  -4/36 .

 

=  6(  (j - 1/3)2 +  17/9 )             Distribute the  6 .

 

=  6(j - 1/3)2 + 34/3

 

Now it is in the form  c(j + p)2 + q  ,  and  q = 34/3  and  p = -1/3  →  q/p  =  (34/3) / (-1/3)  =  -34

hectictar Oct 23, 2017

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