# What is the range of the function #f(x)=(x-1)^2 +2#?

##### 1 Answer

Dec 23, 2017

#### Explanation:

#"the range can be found by finding the maximum or"#

#"minimum turning point of "f(x)#

#"the equation of a parabola in "color(blue)"vertex form"# is.

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

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

#"is a multiplier"#

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

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

#f(x)=(x-1)^2+2larrcolor(blue)"is in vertex form"#

#"with "(h,k)=(1,2)" and a>0#

#"hence "(1,2)" is a minimum turning point"#

#rArr"range is "[2,+oo)#

graph{(x-1)^2+2 [-10, 10, -5, 5]}