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Popular >

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

Solution

range

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

Solution

f (x) \geq - 2

+1

Interval Notation

[- 2, \infty)

Solution steps

Vertex of

x^{2} + 2 x - 1 :

Minimum

(- 1, - 2)

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}) = (- 1, - 2)

f (x) \geq - 2

Popular Examples

extreme 4x^3+6x^2+3x extreme points

4 x^{3} + 6 x^{2} + 3 x

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

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

slope of y^2-10=-4x slope

y^{2} - 10 = - 4 x

midpoint (-3,-5),(-0.5,0)midpoint

(- 3, - 5), (- 0.5, 0)

domain of f(x)=(xsqrt(x))/(2x^2-5)domain

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

Frequently Asked Questions (FAQ)

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