# How do you find the domain and range of #f(x)= x^2- 6x + 8#?

##### 1 Answer

Feb 21, 2018

#### Explanation:

#f(x)" is defined for all real values of x"#

#rArr"domain is "x inRR#

#"to determine the range express "f(x)" in "color(blue)"vertex form"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(f(x)=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a is"#

#"a multiplier"#

#"using the method of "color(blue)"completing the square"#

#f(x)=x^2+2(-3)xcolor(red)(+9)color(red)(-9)+8#

#color(white)(f(x))=(x-3)^2-1#

#rArrcolor(magenta)"vertex "=(3,-1)#

#"to determine if the vertex is a max/min then"#

#• " if "a>0" then vertex is minimum "uuu#

#• " if "a<0" then vertex is maximum "nnn#

#"here "a=1>0rArr" vertex is a minimum"#

#rArr"range is "[-1,+oo)#

graph{x^2-6x+8 [-10, 10, -5, 5]}