Question

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

Answer 1

To find the vertex use -b/2a (for the x value which is also the axis of symmetry)
So 2/-2 = -1 Therefore the axis of symmetry is x=-1 Plug in for the y value:
y= -(-1)^2 -2(-1) + 1 y=-1 + 2 + 1 y=2 Vertex (-1,2)

Answer 2

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