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 $k$?
+9466 k = (6x + 12)(x - 8)
Multiply out the right side of the equation.
k = 6x2 - 48x + 12x - 96
Combine like terms.
k = 6x2 - 36x - 96
In an equation of the form k = ax2 + bx + c with a > 0,
the least possible value of k occurs at \(x\ =\ \text-\frac{b}{2a}\)
So...
In an equation of the form k = 6x2 - 36x - 96 with 6 > 0,
the least possible value of k occurs at \(x\ =\ \text-\frac{(\text-36)}{2(6)}\ =\ \frac{36}{12}\ =\ 3\)
When x = 3, k = 6(3)2 - 36(3) - 96 = 6(9) - 36(3) - 96 = 54 - 108 - 96 = -150
+9466 k = (6x + 12)(x - 8)
Multiply out the right side of the equation.
k = 6x2 - 48x + 12x - 96
Combine like terms.
k = 6x2 - 36x - 96
In an equation of the form k = ax2 + bx + c with a > 0,
the least possible value of k occurs at \(x\ =\ \text-\frac{b}{2a}\)
So...
In an equation of the form k = 6x2 - 36x - 96 with 6 > 0,
the least possible value of k occurs at \(x\ =\ \text-\frac{(\text-36)}{2(6)}\ =\ \frac{36}{12}\ =\ 3\)
When x = 3, k = 6(3)2 - 36(3) - 96 = 6(9) - 36(3) - 96 = 54 - 108 - 96 = -150
