Answer:
1) The vertex is the point
( is a maximum)
2) The function is negative (or is positive for no values of x)
3) The function is decreasing in the interval---------> (-1,∞)
4) The domain is all real numbers
5) The range is all real numbers less than or equal to zero
Step-by-step explanation:
we know that
the equation of a vertical parabola in vertex form is equal to
![y=a(x+h)^{2}+k](https://tex.z-dn.net/?f=y%3Da%28x%2Bh%29%5E%7B2%7D%2Bk)
where
(h,k) is the vertex of the parabola
if
-----> the parabola open upward (vertex is a minimum)
if
-----> the parabola open downward (vertex is a maximum)
in this problem we have
![f(x)=-(x+1)^{2}](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%2B1%29%5E%7B2%7D)
-------> the parabola open downward (vertex is a maximum)
The vertex is the point ![(-1,0)](https://tex.z-dn.net/?f=%28-1%2C0%29)
The domain of the function is the interval---------> (-∞,∞)
The domain is all real numbers
The range of the function is the interval------> (-∞,0]
![y\leq 0](https://tex.z-dn.net/?f=y%5Cleq%200)
The range is all real numbers less than or equal to zero
The function is negative (or is positive for no values of x)
The equation of the axis of symmetry is ![x=-1](https://tex.z-dn.net/?f=x%3D-1)
so
The function is increasing in the interval---------> (-∞,-1)
The function is decreasing in the interval---------> (-1,∞)
see the attached figure to better understand the problem