Mathematics
Chris4457
37

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.

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(1) Answers
CaraTrolinger97

[latex]f(x)=a(x-h)^2+k \Rightarrow \text{vertex}=(h,k)\\\\ f(x)=(x-2)^2+4 \Rightarrow \text{vertex}=(2,4)[/latex] The range of [latex]f(x)=a(x-h)^2+k[/latex] is [latex]y\leq k[/latex] for [latex]a<0[/latex] [latex]y\geq k[/latex] for [latex]a>0[/latex] The domain of any quadratic function is all real numbers. In [latex] f(x)=(x-2)^2+4[/latex], [latex]a=1\ \textgreater \ 0[/latex], so the range is [latex]y\geq4[/latex] So it's D.

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