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That will be a vertical line that passes through the parabola at the point where it's slope is equal to zero.

The first step then, is to take the derivative of the curve with respect to x:

y = x2 + 2x + 6

dy/dx = 2x + 2

Then let dy/dx equal zero, and solve for x:

0 = 2x + 2

2x = -2

x = -1

So the axis of symmetry is the line x = -1.

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