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

##### 1 Answer

Aug 31, 2017

#### 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]}