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Popular >

range of f(x)=-x^2-2x-1

Solution

range

f (x) = - x^{2} - 2 x - 1

Solution

f (x) \leq 0

+1

Interval Notation

(- \infty, 0]

Solution steps

Vertex of

- x^{2} - 2 x - 1 :

Maximum

(- 1, 0)

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = - 1,

Vertex

(x_{v}, y_{v}) = (- 1, 0)

f (x) \leq 0

Popular Examples

asymptotes of (2x)/(x^2-9)asymptotes

\frac{2 x}{x ^{2} - 9}

f (x) = - 2

range of 2x^2 range

2 x^{2}

asymptotes of 1/(5-x)asymptotes

\frac{1}{5 - x}

distance (0,0),(-3,4)distance

(0, 0), (- 3, 4)

Frequently Asked Questions (FAQ)

What is the range of f(x)=-x^2-2x-1 ?
The range of f(x)=-x^2-2x-1 is f(x)<= 0