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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 $k$?

 Jul 12, 2019

Best Answer 

 #1
avatar+8852 
+5

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

 

Check: https://www.desmos.com/calculator/cgenn1yfoy

 Jul 12, 2019
 #1
avatar+8852 
+5
Best Answer

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

 

Check: https://www.desmos.com/calculator/cgenn1yfoy

hectictar Jul 12, 2019

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