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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

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askme1972

Answer:

C.

Step-by-step explanation:

Jennifer completed the square by adding 1.  However, to keep both sides equal, she should have added 1 to both sides:

y + 1 = (x² + 2x + 1) + 7

Or, she should have added 1 and subtracted 1 from the same side.

y = (x² + 2x + 1) + 7 − 1

The correct vertex form of the equation is:

y = (x + 1)² + 6