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

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Answer 1 · 2016-03-26T12:19:23

Domain: $(- \infty, + \infty)$ $(-oo, +oo)$
Range: $[6, + \infty)$ $" "[6, +oo)$

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

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

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

Vertex is at $(1, 6)$ $(1, 6)$

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

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

How do you find the domain and range of p(x)=x^2-2x+7p(x)=x2−2x+7 p(x)=x^2-2x+7?