Answer:
The vertex is (-1, 0),
The function is increasing and decreasing both for different intervals,
The domain of the function is set of all real numbers,
Range is (-∞, 0]
Step-by-step explanation:
Given function,
[tex]f(x)=-x^2 - 2x - 1[/tex]
[tex]f(x) = -(x^2 + 2x+1)[/tex]
[tex]f(x) = -(x+1)^2+0[/tex]
Since, vertex form of a quadratic equation is,
[tex]f(x) = a(x-h)^2 + k[/tex]
Where,
(h, k) is the vertex of the function,
By comparing,
Vertex of the given function = (-1, 0),
A quadratic function with negative leading coefficient is increasing from -∞ to its vertex and decreasing from its vertex to +∞,
Also, domain of a quadratic function is set of all real numbers,
While, quadratic function with negative leading coefficient is maximum at its vertex,
∴ Range = (-∞, 0]
