Question

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

Answer 1

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

Answer 2

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

Answer 3

what do u think

Answer 4

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.

Answer 5

\[\large\rm f(x)=3(x^2+2x+1)-7\color{orangered}{-3}\]\[\large\rm f(x)=3(x+1)^2-10\]Do you see where the mistake was made? :)