Question

use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1. the vertex is the . the function is increasing . the function is decreasing . the domain of the function is . the range of the function is .

Answer 1

The vertex is the . maximum value

The function is increasing . when x < -1

The function is decreasing . when x >-1

The domain of the function is . all real numbers

The range of the function is all numbers less than or equal to 0

Step-by-step explanation: edg

Answer 2

The vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.

Explanation:

The given function is

`f(x)=-x^2-2x-1`

`f(x)=-[x^2+2x+1]`

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

The general vertex form of the parabola is

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

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

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

`a=-1`

`h=-1`

`k=0`

The vertex of the parabola is (-1,0). Since a=-1<1 so it is a downward parabola.

The axis of symmetry is x=-1. So, before -1 the function is increasing and after -1 the function is decreasing.

The vertex of a downward parabola is the point of maxima. So, the rang of the function can not exceed 0.

Therefore the vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.