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

Step-by-step explanation:

We are given the quadratic function f(x) = -1x^2 - 2x - 1, which factors into:

f(x) = -1(x + 1)(x + 1) = -(x + 1)^2.  Comparing this to the vertex equation of a quadratic, we get:

f(x) = -(x + 1)^2 + 0

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

where (h, k) represents the vertex.  We see readily that h = -1, k = 0 and a = -1.  The vertex is at (-1, 0), and the graph of this quadratic/parabola opens down (because a is negative).  The vertex lies on the x-axis 1 unit to the left of the y-axis.

Quickly sketch this parabola.  It begins in Quadrant III and ends in Quadrant IV.  From this sketch we can see that the function is increasing on the interval (-infinity, -1), at its maximum at (-1, 0) and decreasisng on the interval (-1, infinity).

Quadratic functions are defined for all x, so the domain of this one is

(-infinity, infinity).  

As we have seen, the maximum value this function can have is zero (0).  Therefore, the range (which represents all possible y values) is

(-infinity, 0).

answer: 2 and 1

step-by-step explanation: got this question