Question

What is the domain and range of `y = (x – 5)^2 + 10`?

Answer 1

Domain: `{x|x in RR}`

Range: `{y|y in RR, y>=10}`

Explanation:

You will notice that it is a quadratic equation in "vertex form":

`y=(x+h)^2 +k`

In vertex form the vertex is `(-h,k)`

`y = (x – 5)^2 + 10`

vertex `=(5,10)`

Domain; all quadratic functions have a domain of all real numbers:

Domain: `{x|x in RR}`

Range, since `x` is positive the function opens up and the vertex is a minimum, the `y=10` so the range is:

Range: `{y|y in RR, y>=10}`