Question

How do you solve `x^2+4x+4>=9` using a sign chart?

Answer 1

the answer is `x in(-oo,-5)uu(1,+oo)`

Explanation:

`x^2+4x+4>=9`
so `x^2+4x-5>=0`
Factorising `(x-1)(x+5)>=0`
The values we are looking at are `x=1` and `x=-5`

the sign chart is the following

`x` `color(white)(aaaaaaaaaaa)` `-oo` `color(white)(aaaaaa)` `-5` `color(white)(aaaaaa)` `1` `color(white)(aaaaaa)` `+oo`
`x-1` `color(white)(aaaaaaaaaaaaa)` `-` `color(white)(aaaaaa)` `-` `color(white)(aaaaa)` `+`
`x+5` `color(white)(aaaaaaaaaaaaa)` `-` `color(white)(aaaaaa)` `+` `color(white)(aaaaa)` `+`
`(x-1)(x+5)` `color(white)(aaaaaa)` `+` `color(white)(aaaaaa)` `-` `color(white)(aaaaa)` `+`

From the sign chart, we see that `x in (-oo,-5)` for the function to be positive
From the sign chart, we see that `x in (1,+oo)` for the function to be positive