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

Domain: $\left(- \infty , + \infty\right)$
Range:$\text{ } \left[6 , + \infty\right)$

#### Explanation:

This is a parabola $p \left(x\right) = {x}^{2} - 2 x + 7$

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

$p \left(x\right) = {x}^{2} - 2 x + 1 - 1 + 7$
$p \left(x\right) = {\left(x - 1\right)}^{2} + 6$
$p \left(x\right) - 6 = {\left(x - 1\right)}^{2}$

Vertex is at $\left(1 , 6\right)$

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

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