The equation for a general quadratic is `y=ax^2+bx+c` . The shape of the graph is a parabola.

The vertex has x-coordinate `x=-b/(2a)` and the equation for the axis of symmetry is also `x=-b/(2a)` .

For `y=-x^2` we have a=-1,b=c=0. The axis of symmetry is x=0. The vertex has x-coordinate 0, so y=0 and the vertex is at (0,0).

The graph is the same as that of `y=x^2` only reflected across the x-axis.

The graph:

The vertex is at (0,0) and the axis of symmetry is the y-axis or x=0.

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