Question

Which graph represents the function f(x) = (x – 5)2 + 3?

Answer 1

we have

$f(x)=(x-5)^{2}+3$

This is a quadratic equation (vertical parabola) open up

The vertex is a minimum--------> vertex is the point $(5,3)$

The domain of the function is all real numbers------> interval (-∞,∞)

The range of the function is the interval--------> [3,∞)

The axis of symmetry is the x coordinate of the vertex

so

the axis of symmetry is $x=5$

therefore

the answer in the attached figure

Answer 2

The function
$f(x)=(x-5)^2+3$
describes a parabola with vertex = (5, 3).

The graph of the function is attached.