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

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

Explanation:

Answer 2

`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.