Question

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.

Answer 1

The correct option is 2.

Explanation:

The given function is

`f(x)=-(x+1)^2+4` ..... (1)

The standard form of a parabola is

`y=a(x-h)^2+k` .....(2)

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

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

`h=-1`

`k=4`

`a=-1`

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.

Answer 2

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