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 inc

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grigory

1 month ago

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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 inc

reasing . the function is decreasing . the domain of the function is . the range of the function is .

Mathematics

2 answers:

PIT_PIT [12.4K] · Answer 1 · 2026-02-25T12:25:09+03:00

Answer:

The peak of the parabola indicates the highest point, which is(-1,0). The function is rising for x <-1 and declining for x >-1. The domain covers all real numbers. The function’s range encompasses all real numbers up to and including 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 standard vertex form of the parabola is

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

Where (h,k) denotes the vertex and a represents the stretch factor.

Upon comparing (1) and (2), we find

$a=-1$

$h=-1$

$k=0$

The vertex of the parabola is (-1,0). Given that a=-1<1, we confirm this is a parabola that opens downward.

The line of symmetry is x=-1. Thus, the function increases prior to -1 and decreases thereafter.

The vertex on a downward-facing parabola signifies the maximum point. As a result, the function's range cannot exceed 0.

<pThus, the vertex represents the highest point, i.e.,(-1,0). The function ascends when x<-1 and descends when x>-1. The domain includes all real numbers. The range is all real numbers less than or equal to 0.