+80 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?
+129852 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
