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Popular >

range of-x^2-2x-1

Solution

range

- 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

domain of f(x)=0.5(2)^x domain

f (x) = 0.5 (2)^{x}

domain of sqrt(x^2-3)domain

x^{2} - 3

domain of 9-4x^2 domain

9 - 4 x^{2}

distance (-3,2),(2,-2)distance

(- 3, 2), (2, - 2)

intercepts of f(x)=-1/2 (x-1/3)^2-3/2 intercepts

f (x) = - \frac{1}{2} (x - \frac{1}{3})^{2} - \frac{3}{2}

Frequently Asked Questions (FAQ)

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