The expression we have is:
[tex]y=-x^2-7[/tex]We need to compare this equation of our parabola, with the general equation of a parabola in vertex form:
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex of the parabola, and a indicates if the parabola opens up or opens down (if a is positive the parabola opens up, and if a is negative the parabola opens down).
We take our equation:
[tex]y=-x^2-7[/tex]And we arrange the terms so that it looks like the vertex form:
[tex]y=(-1)(x-0)^2+(-7)[/tex]And we can find the values of a, h, and k:
[tex]\begin{gathered} a=-1 \\ h=0 \\ k=-7 \end{gathered}[/tex]We only need h and k for the vertex:
[tex](h,k)=(0,-7)[/tex]Answer: the vertex is at (0,-7)
