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If we express $3x^2 + x - 4$ in the form $a(x - h)^2 + k$, then what is $k$?

 Jan 21, 2018
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3x^2 + x - 4   factor out the 3

 

3( x^2 + (1/3)x  -  4/3 )

 

Take 1/2 of 1/3  = 1/6  .....square this  = 1/36....add and subtract it within the parentheses

 

3(x^2  + (1/3)x  + 1/36   -  4/3  -1/36 ) 

 

Factor the first three terms in the parentheses and simplify

 

3  (   [ x + 1/6 ]^2  -  48/36  -  1/36 )

 

3 ( [ x + 1/6 ] ^2  - 49/36 )

 

3(x + 16)^2 -  49/12 

 

So.... k  =  -49/12

 

 

cool cool cool

 Jan 21, 2018

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