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Popular >

range of f(x)=2x^2-4x-1

Solution

range

f (x) = 2 x^{2} - 4 x - 1

Solution

f (x) \geq - 3

+1

Interval Notation

[- 3, \infty)

Solution steps

Vertex of

2 x^{2} - 4 x - 1 :

Minimum

(1, - 3)

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 = 2,

Vertex

(x_{v}, y_{v}) = (1, - 3)

f (x) \geq - 3

Popular Examples

inverse of x^2-6x+11 inverse

x^{2} - 6 x + 11

range of f(x)=-sqrt(81-x^2)range

f (x) = - 81 - x^{2}

inverse of f(x)= 1/3 (x-2.1)^2+7.9 inverse

f (x) = \frac{1}{3} (x - 2.1)^{2} + 7.9

line y=-x/4+5 line

y = - \frac{x}{4} + 5

inverse of f(x)=(x+8)^2 inverse

f (x) = (x + 8)^{2}

Frequently Asked Questions (FAQ)

What is the range of f(x)=2x^2-4x-1 ?
The range of f(x)=2x^2-4x-1 is f(x)>=-3