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Popular Functions >

range of 2x^2+4x-1

Solution

range

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

Graph

Popular Examples

slope ofintercept 2x+y=-5

range of f(x)=sqrt(4x-7)

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

extreme x^3-48x+7

inverse of sqrt(8-x)+7

Frequently Asked Questions (FAQ)

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