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The quadratic 10x^2+100x+1000$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?

 May 22, 2019
 #1
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10x^2+100x+1000      factor  out  10

 

10 ( x ^2 +10x + 100)      complete the square on x

 

10 (x^2 +10x + 25 + 100 - 25 )        factor the first three terms in the parenthses.....simplify the rest

 

10 [ (x + 5)^2  + 75 ]

 

10 ( x + 5)^2 + 750

 

a = 10    b  = 5     c  = 750

 

So

 

a + b + c  =   10 + 5 + 750  =  765

 

 

cool cool cool

 May 22, 2019

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