Question

How do you find the domain and range of `h(x) = (x - 2)^2 + 2`?

Answer 1

`x inRR,y in[2,oo)`

Explanation:

`"This is a polynomial of degree 2 and is well defined for all"`
`"real values of "x`

`"domain is "x inRR`

`(-oo,+oo)larr color(blue)"in interval notation"`

`"To obtain the range we require the vertex and whether"`
`"it is a max/min turning point"`

`"The equation of a parabola in "color(blue)"vertex form"` is.

`•color(white)(x)y=a(x-h)^2+k`

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

`y=(x-2)^2+2" is in this form"`

`color(magenta)"vertex "=(2,2)`

`"Since "a>0" then minimum turning point "uuu`

`"range is "y in[2,+oo)`
graph{(x-2)^2+2 [-10, 10, -5, 5]}