The vertex form:
[tex]f(x)=a(x-h)^2+k\\\\(h,\ k)-vertex[/tex]
We have the vertex (-2, -1) → h = -2 and k = -1. Substitute:
[tex]f(x)=a(x-(-2))^2+(-1)=a(x+2)^2-1[/tex]
We have the y-intercept (0, -9). Substitute f(x) = -9 and x = 0:
[tex]-9=a(0+2)^2-1[/tex] add 1 to both sides
[tex]-8=a(2)^2[/tex]
[tex]-8=4a[/tex] divide both sides by 4
[tex]-2=a\to a=-2[/tex]
Answer: [tex]\boxed{f(x)=-2(x+2)^2-1=-2x^2-8x-9}[/tex]
