Question Regarding Completing the Square to find the minimum of Parabola

GRE Quant Problem Solving
1

I went through the Week 2, Day 7 Graphing Functions Video of the 2 Month Plan. Towards the end Greg Solved a Question about finding the minimum of the Parabola. The equation was

y=x²+6x-16

One of the callers called in to add and subtract 9 to make it (x+3)² -25 but my concern was that it could also complete into (x-3)² -7. Which gives us 2 centers of the same parabola and different minimums. So in this case what would happen ?

2

They’re different; try expanding those 2 and see if they both match or not.

3

Right, Thanks a lot