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

Answer 1

In line two, Madlime added positive one in the bracket, but subtracted one outside of the bracket without considering the factor outside of the bracket. Therefore, line 2 should be f(x)=3(x2+2x+1-1)-7
Line 3: f(x)=3(x+1)2-7-3
Line 4: f(x)=3(x+1)2-10

Answer 2

Madeline made a mistake in LINE 2

Explanation:

We are given:

f(x) = 3x² + 6x − 7

Line 1: f(x) = 3(x² + 2x) − 7

Line 2: f(x) = 3(x² + 2x + 1 - 1) - 7

= 3(x²+2x+1) -7 - 3

But Madeline wrote it 3(x² + 2x + 1) − 7 − 1

So, she made a mistake here

Line 3: f(x) = 3(x + 1)² − 10

So, Madeline made a mistake in LINE 2 and because of this LINE 3 was also wrong