anonymous
  • anonymous
Madeline was completing the square, and her work is shown below. Identify the line where she made her mistake. f(x) = 3x2 + 6x − 7 Line 1: f(x) = 3(x2 + 2x) − 7 Line 2: f(x) = 3(x2 + 2x + 1) − 7 − 1 Line 3: f(x) = 3(x + 1)2 − 8 Line 1 Line 2 Line 3 She did not make any mistakes
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I think line 1 because it should be 3x on both sides not 2. but u should get a second opinion
zepdrix
  • zepdrix
Line 1 looks ok :) Madeline factored a 3 out of each of the first two terms.
Ashely14
  • Ashely14
what do u think

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zepdrix
  • zepdrix
To complete the square, she recognized that she needed a +1\[\large\rm f(x)=3(x^2+2x+1)-7\]But you have to balance this by also subtracting 1. But the subtraction needs to happen inside of the brackets!\[\large\rm f(x)=3(x^2+2x+1\color{orangered}{-1})-7\]In order for this -1 to come outside of the brackets, it needs to multiply the 3.
zepdrix
  • zepdrix
\[\large\rm f(x)=3(x^2+2x+1)-7\color{orangered}{-3}\]\[\large\rm f(x)=3(x+1)^2-10\]Do you see where the mistake was made? :)

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