en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

range

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

Solution

f (x) \geq - \frac{1}{4}

+1

Interval Notation

[- \frac{1}{4}, \infty)

Solution steps

Vertex of

x^{2} - x :

Minimum

(\frac{1}{2}, - \frac{1}{4})

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}) = (\frac{1}{2}, - \frac{1}{4})

f (x) \geq - \frac{1}{4}

Popular Examples

inverse of y=log_{7}(2x-5)+9 inverse

y = lo g_{7} (2 x - 5) + 9

inverse of (-3x-3)/(x-1)inverse

\frac{- 3 x - 3}{x - 1}

range of f(x)= x/(-8x+3)range

f (x) = \frac{x}{- 8 x + 3}

domain of F(t)= t/(|t|)domain

F (t) = \frac{t}{∣ t ∣}

line (0,0),(2,2)line

(0, 0), (2, 2)

Frequently Asked Questions (FAQ)

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