Question

How do you find the domain and range of `p(x)=x^2-2x+7`?

Answer 1

Domain: `(-oo, +oo)`
Range:`" "[6, +oo)`

Explanation:

This is a parabola `p(x)=x^2-2x+7`

We solve for the vertex to determine the minimum point, because this parabola opens upward.

`p(x)=x^2-2x+1-1+7`
`p(x)=(x-1)^2+6`
`p(x)-6=(x-1)^2`

Vertex is at `(1, 6)`

graph{y=x^2-2x+7[-20,20,-10,10]}

God bless....I hope the explanation is useful.