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

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

anonymous · Answer

In line 1 she should have factored a 3 out -7.  The equation would look like this:
$$f(x)=3(x ^{2}+2x-\frac{ 7 }{ 3 })$$