Question

Write into vertex form. y = -x^2 -2x -3

Answer 1

The vertex form of
`f(x)=ax^2+bx+c`

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

where:
`h=(-b)/(2a);\ k=f(h)`

We have:
`f(x)=-x^2-2x-3\to a=-1;\ b=-2;\ c=-3`

substitute:

`h=(-(-2))/(2\cdot(-1))=(2)/(-2)=-1\\\\k=f(-1)=-(-1)^2-2\cdot(-1)-3=-1+2-3=-2`
The vertex form of f(x):

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