[tex]y= -\frac{1}{2} x^{2}-1[/tex] is a quadratic function, so its graph is a parabola.
Notice that the coefficient of x is 0, this always means that the axis of symmetry is the y-axis.
That is, the vertex of the parabola is in the y-axis, so the x-coordinate of the vertex is 0.
for x=0, y=-1. So the vertex is (0, -1)
The coefficient of [tex] x^{2} [/tex] is negative. This means that the parabola opens downwards, so the vertex is a maximum.
Answer: (0, -1) , maximum (none of the choices)
