Answer:
The vertex is (2, 4), the domain is all real numbers, and the range is y≥ 4
Step-by-step explanation:
we have
[tex]f(x)=(x-2)^{2}+4[/tex]
This is the equation of a vertical parabola in vertex form
[tex]f(x)=a(x-h)^{2}+k[/tex]
where
a is a coefficient
(h,k) is the vertex
if a > 0 the parabola open upward and the vertex is a minimum
if a < 0 the parabola open downward and the vertex is a maximum
In this problem we have
a=1
so
the parabola open upward and the vertex is a minimum
The vertex is the point (2,4)
The domain is the interval -----> (-∞,∞)
The domain is all real numbers
The range is the interval ----> [4,∞)
[tex]y\geq 4[/tex]
The range is all real numbers greater than or equal to 4
