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Popular >

range of x^2+4x-1

Solution

range

x^{2} + 4 x - 1

Solution

f (x) \geq - 5

+1

Interval Notation

[- 5, \infty)

Solution steps

Vertex of

x^{2} + 4 x - 1 :

Minimum

(- 2, - 5)

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}) = (- 2, - 5)

f (x) \geq - 5

Popular Examples

extreme f(x)=xe^{1/x}extreme points

f (x) = x e^{\frac{1}{x}}

inverse of f(x)=(9x-1)/(2x+4)inverse

f (x) = \frac{9 x - 1}{2 x + 4}

slope ofintercept 2x-9y-4=0 slope intercept

2 x - 9 y - 4 = 0

domain of f(x)=ln(((|x|-1))/(x^2-2))domain

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

domain of f(x)= 3/(sqrt(x-13))domain

f (x) = \frac{3}{x - 13}

Frequently Asked Questions (FAQ)

What is the range of x^2+4x-1 ?
The range of x^2+4x-1 is f(x)>=-5