Find allgebraiclly the equation of the axis of symmetry and the vertex of the parabola represented by the equation y=-x2-2x+1

The vertex can be found by finding when the derivative is equal to zero (velocity is zero)

dy/dx=-2x-2

dy/dx=0 when -2x-2=0, -2x=2, x=-1

y(-1)=-(-1^2)-2(-1)+1

y(-1)=-1+2+1=2

So the vertex is at the point (-1,2) and the axis of symmetry is the line:

x=-1

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