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Popular Functions >

range of 2x^2-1

Solution

range

2 x^{2} - 1

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

2 x^{2} - 1 :

Minimum

(0, - 1)

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}) = (0, - 1)

f (x) \geq - 1

Graph

Popular Examples

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extreme f(x)=-x^3-48x

Frequently Asked Questions (FAQ)

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