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