Question

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

Answer 1

`[2,+oo)`

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]}