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Popular >

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

Solution

range

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

Solution

f (x) \geq 2

+1

Interval Notation

[2, \infty)

Solution steps

Vertex of

(x - 2)^{2} + 2 :

Minimum

(2, 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}) = (2, 2)

f (x) \geq 2

Popular Examples

extreme f(x)=x^2+5x-2 extreme points

f (x) = x^{2} + 5 x - 2

extreme f(x)=-3x^4-8x^3-6x^2+1 extreme points

f (x) = - 3 x^{4} - 8 x^{3} - 6 x^{2} + 1

critical f(x)=3x^2+16x critical points

f (x) = 3 x^{2} + 16 x

domain of f(x)=sqrt(8+5x)domain

f (x) = 8 + 5 x

range of cos(2φ)range

cos (2 φ)

Frequently Asked Questions (FAQ)

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