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

 Aug 9, 2020
 #1
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3ax2 + 3bx + 3c

 

Factor out the 3:           3[ ax2 + bx + c ]

Factor out the a:           3[ a( x2 + (b/a)x ) + c ]

Complete the square:  3[ a( x2 + (b/a)x + b2/(4a)2 ) + c - b2/(4a) ]

Factor:                         3[ a( (x + b/(2a) )2 ) + ( c - b2/(4a) )]

Multiply back the 3:         3a( (x + b/(2a) )2 ) + ( 3c - 3b2/(4a) )

 

n = 3a         h  =  -b/(2a)     k  =  3c - 3b2/(4a)

 Aug 10, 2020

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