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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.

Verified Answer :

konrad509

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

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

Answer:

The answer is D. The vertex is (2,4), the domain is all real numbers, and the range is y is greater than or equal to 4

Step-by-step explanation:

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