# What is the range of the function #f(x) = 9x^2 - 9x#?

##### 1 Answer

Apr 23, 2018

#### Explanation:

#"since the leading coefficient is positive "#

#f(x)" will be a minimum "uuu#

#"we require to find the minimum value"#

#"find the zeros by setting "f(x)=0#

#rArr9x^2-9x=0#

#"take out a "color(blue)"common factor "9x#

#rArr9x(x-1)=0#

#"equate each factor to zero and solve for x"#

#9x=0rArrx=0#

#x-1=0rArrx=1#

#"the axis of symmetry is at the midpoint of the zeros"#

#rArrx=(0+1)/2=1/2#

#"substitute this value into the equation for minimum value"#

#y=9(1/2)^2-9(1/2)=9/4-9/2=-9/4larrcolor(red)"min. value"#

#rArr"range "y in[-9/4,oo)#

graph{9x^2-9x [-10, 10, -5, 5]}