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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 sqrt(x+2)-6 inverse

x + 2 - 6

inverse of f(x)=x^3+9 inverse

f (x) = x^{3} + 9

inverse of f(x)=(x-5)/(2x+3)inverse

f (x) = \frac{x - 5}{2 x + 3}

domain of ((1-x))/(sqrt(1-x^2))domain

\frac{( 1 - x )}{1 - x ^{2}}

inverse of f(x)=2cos(x)inverse

f (x) = 2 cos (x)

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