Jennifer made an error converting y=x^2+2x+7 to vertex form. In which step did she make the error? Explain your answer and provide the correct form of the equation in vertex form.

A. y=x^2+2x+7
B. y=(x^2+2x)+7
C. y=(x^2+2x+1)+7
D. y=(x+1)^2+7

SERIOUS ANSWERS ONLY

Answer and Step-by-step explanation:

The step that was wrong is at C: when Jennifer added the 1 into the parentheses, she forgot to subtract 1 from the 7. The reason she needs to do that is because now, if you compare her equation at C with her original, they're not the same:

Original: x^2 + 2x + 7

Step C: x^2 + 2x + 8

So, Jennifer actually needs to subtract 1 from the 7 if she wants to add 1 into the parenthetical expression:

Correct Step C: (x^2 + 2x + 1) + 7 - 1 = (x^2 + 2x + 1) + 6

Now, the correct vertex form is: (x + 1)^2 + 6

Hope this helps!

She made a mistake in step C.

C) y=(x²+2x+1)+7-1

D) y=(x+1)²+6