Question

For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range. a. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≥ 4. b. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≤ 4. c. The vertex is (2, 4), the domain is all real numbers, and the range is y ≤ 4. d.The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.

Answer 1

$f(x)=a(x-h)^2+k \Rightarrow \text{vertex}=(h,k)\\\\ f(x)=(x-2)^2+4 \Rightarrow \text{vertex}=(2,4)$

The range of $f(x)=a(x-h)^2+k$ is
$y\leq k$ for $a$
$y\geq k$ for $a>0$

The domain of any quadratic function is all real numbers.

In $f(x)=(x-2)^2+4$, $a=1\ \textgreater \ 0$, so the range is $y\geq4$

So it's D.