Question

What is the range of the function `f(x)=x^2-x-2`?

Answer 1

`[-9/4,+oo)`

Explanation:

`"complete the square on f(x)"`

`f(x)=x^2-2(1/2)x+1/4-1/4-2`

`color(white)(f(x))=(x-1/2)^2-9/4`

`"for all x",(x-1/2)^2>=0`

`"the minimum value of f(x) is therefore "-9/4`

`rArr"range is "[-9/4,+oo)`
graph{x^2-x-2 [-10, 10, -5, 5]}