Question

The vertex is (-2,-1) the y intercept is (0,-9) whats the function?

Answer 1

The vertex form:

`f(x)=a(x-h)^2+k\\\\(h,\ k)-vertex`

We have the vertex (-2, -1) → h = -2 and k = -1. Substitute:

`f(x)=a(x-(-2))^2+(-1)=a(x+2)^2-1`

We have the y-intercept (0, -9). Substitute f(x) = -9 and x = 0:

`-9=a(0+2)^2-1` add 1 to both sides

`-8=a(2)^2`

`-8=4a` divide both sides by 4

`-2=a\to a=-2`

Answer:
`\boxed{f(x)=-2(x+2)^2-1=-2x^2-8x-9}`