Answer:
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.
Step-by-step 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.
