## anonymous one year ago 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

1. anonymous

I think line 1 because it should be 3x on both sides not 2. but u should get a second opinion

2. zepdrix

Line 1 looks ok :) Madeline factored a 3 out of each of the first two terms.

3. Ashely14

what do u think

4. 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.

5. 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? :)