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The quadratic ax^2 + bx + c can be expressed in the form 2(x - 8)^2 + 4. When the quadratic 3ax^2 + 2bx + c is expressed in the form n(x - h)^2 + k, what is h?

 Apr 12, 2022
 #1
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2(x - 8)^2  + 4   =

2 (x^2 - 16x + 64) + 4  =

2x^2 - 32x + 128 + 4  =

2x^2 -32x + 132

 

a = 2

b = -32

c = 132

 

So

 

3ax^2  + 2bx + c  =

 

6x^2- 64x + 132         

 

6  [ x^2 - (32/3)x + 22]       complete the square on the terms in the brackets

 

                                           Note : ([ 32/3] [1/2]) =  (16/3)^2   =256/9

 

6 [ x^2 - (32/3)x  + 256/9  + 22 - 266/9 ]  =

 

6 [ (x - (16/3)]^2  +  6 [ -58/9]  =

 

6 [ x - (16/3) ]^2  -116/3

 

h  = 16/3

 

cool cool cool

 Apr 12, 2022

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