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If we express 2x^2 + 6x + 11 in the form a(x - h)^2 + k, then what is h?

 Jun 29, 2021
 #1
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2 (x^2 +3x)   = -11

2 (x+1.5)^2 = -11 + 2.25       You can finish, right?

 Jun 29, 2021
 #2
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$ 2x^2+6x+11  $

 

$ 2\left(x^2+3x+\frac{11}{2}\right)  $

 

$ 2n=3 \implies n=\frac{3}{2} $ which you want to square $ \implies \left(\frac{3}{2}\right)^2 $

 

$ 2\left(x^2+3x+\frac{11}{2}+\left(\frac{3}{2}\right)^2\right) =2 \left( \left(\frac{3}{2}\right)^2 \right) $

 

$ 2\left(x^2+3x+\frac{11}{2}+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2\right)  $

 

completing the square 

 

$ 2\left(\left(x+\frac{3}{2}\right)^2+\frac{11}{2}-\left(\frac{3}{2}\right)^2\right)   \implies  2\left(\left(x+\frac{3}{2}\right)^2\right) + 2\left( \frac{11}{2}-\frac{9}{4} \right) $

 

           $\Updownarrow   $

 

$ 2\left(x+\frac{3}{2}\right)^2+\frac{26}{4} \equiv a(x - h)^2 + k $ 

 

$ \overset{. \: .}{\smile } $

 Jun 29, 2021

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