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What value of x will give the minimum value for x^2 + 11x - 5 + 5x

 Feb 9, 2022
 #1
avatar+23200 
+2

Rewrite to find the vertex:

y  =  x2 + 11x - 5 + 5x

y  =  x2 + 16x - 5

y  =  (x2 + 16x + .....) - 5

Complete the square:  (divide the coefficient of the x-term by 2 and square the answer):

y  =  (x2 + 16x + 64) - 5 - 64

y  =  (x + 8)2 - 69

The mininum will occur when x = -8; it is -69.

 Feb 9, 2022
 #2
avatar+36434 
+1

= x^2 + 16x -5      bowl shaped parabola,  min will occur at x = - b/2a = -16/(2*1) = - 8  ,  sub in '-8' for x to find the minumum value of  -69

 Feb 10, 2022

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