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]}
