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for the function f(x) = –(x 1)2 4, identify the vertex, domain, and range. the vertex is (–1, 4), the domain is all real numbers, and the range is y ≥ 4. the vertex is (–1, 4), the domain is all real numbers, and the range is y ≤ 4. the vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4. the vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.

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nobillionaireNobley
f(x) = -(x + 1)^2 + 4
Vertex = (-1, 4)
Domain is all real numbers.
Range is f(x) <= 4

Answer:

The correct option is 2.

Step-by-step explanation:

The given function is

[tex]f(x)=-(x+1)^2+4[/tex]                     ..... (1)

The standard form of a parabola is

[tex]y=a(x-h)^2+k[/tex]                       .....(2)

Where, (h,k) is the vertex and a is stretch factor.

On comparing (1) and (2), we get

[tex]h=-1[/tex]

[tex]k=4[/tex]

[tex]a=-1[/tex]

The vertex of the parabola is (-1,4). Since a=-1<0, therefore it is a downward parabola. Domain of an downward parabola is all real numbers.

The vertex of a downward parabola is the point of maxima. So the range of the function can not be more that 4.

Therefore  the domain is all real numbers, and the range is y ≤ 4. Option 2 is correct.

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