we know that
If an axis of symmetry is \(x=-8\) and has a maximum height of \(2\)
then
Is a vertical parabola open down with vertex at \((-8,2)\)
the equation in vertex form is equal to
\(y=a(x-h)^{2}+k\)
where
(h,k) is the vertex
substitute
\(y=a(x+8)^{2}+2\)
Find the value of a
the parabola passes through the point \((-7,-1)\)
substitute in the formula
\(-1=a(-7+8)^{2}+2\)
\(-1=a(1)^{2}+2\)
\(-1=a+2\)
\(a=-3\)
therefore
the answer is
the equation in vertex form is \(y=-3(x+8)^{2}+2\)
