If you analyse this you would see,

when x = -4, y = -1

and x = -10 also, y = -1

That means at -4 and -10, the parabola has same value and it is symmetrical in the middle point of [-4,-10] range.

The middle point is = (-4 -10)/2

= -7

Therefore the axis of symmetry is x = -7 or x+7 =0

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