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

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The best and most correct answer among the choices provided by the question is Line 2.       
    
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Answer 2

Answer:

Line 2

Step-by-step explanation:

Madeline was completing the square, and her work is shown below

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

$f(x) = 3x^2 + 6x - 7$

In completing the square method we need x^2 alone

Take out 3 from first two terms

$f(x) = (3x^2 + 6x) - 7$

$f(x) = 3(x^2 + 2x) - 7$

In completing the square method, we take middle term 2 , divide by 2 and then square it

2/2 =1

1^2 = 1

Now add and subtract 1

$f(x) = 3(x^2 + 2x +1 - 1) - 7$

Take out -1 , multiply with 3

$f(x) = 3(x^2 + 2x +1) -3- 7$

$f(x) = 3(x^2 + 2x +1) -10$

Madeline made a mistake in Line 2 . she forgot to multiply 3 with -1