en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of 3(x-1)^2-2

Solution

range

3 (x - 1)^{2} - 2

Solution

f (x) \geq - 2

+1

Interval Notation

[- 2, \infty)

Solution steps

Vertex of

3 (x - 1)^{2} - 2 :

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 = 3,

Vertex

(x_{v}, y_{v}) = (1, - 2)

f (x) \geq - 2

Popular Examples

inflection (x-x^2)/((x+1)^2)inflection points

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

inverse of y=sqrt(x+2)+3 inverse

y = x + 2 + 3

midpoint (2,0),(0,-2)midpoint

(2, 0), (0, - 2)

shift 4sin(3pi-2pix)-7pi shift

4 sin (3 π - 2 π x) - 7 π

extreme f(x)=3x^3-81x extreme points

f (x) = 3 x^{3} - 81 x

Frequently Asked Questions (FAQ)

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