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In an equation of the form k = ax^2 + bx + c with a > 0, the least possible value of k occurs at x = -b/(2a). In the equation k = (6x + 12)(x - 8), what is the least possible value for k?

 Dec 26, 2018
 #1
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k =  (6x + 12) (x - 8)      expand

 

k =  6x^2 + 12x - 48x - 96     simplify

 

k = 6x^2  - 36x - 96

 

The value of x that minimizes k can be found as

 

- (-36) / [ 2 * 6 ]    =    36  / 12 =  3

 

Put this back into the function

 

6(3)^2 - 36 (3) - 96   =

 

6 * 9 - 108 - 96

 

54 - 108 - 96  = 

 

- 150   =  minimum value of k

 

 

cool cool cool

 Dec 26, 2018

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