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Popular >

range of f(x)=(x-3)^2+2

Solution

range

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

Solution

f (x) \geq 2

+1

Interval Notation

[2, \infty)

Solution steps

Vertex of

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

Minimum

(3, 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}) = (3, 2)

f (x) \geq 2

Popular Examples

extreme f(x)=-2x^3-27x^2-84x-3 extreme points

f (x) = - 2 x^{3} - 27 x^{2} - 84 x - 3

intercepts of f(x)=x^2-6x+7 intercepts

f (x) = x^{2} - 6 x + 7

domain of f(x)=6x+2 domain

f (x) = 6 x + 2

inverse of f(x)=10-4x inverse

f (x) = 10 - 4 x

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

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

Frequently Asked Questions (FAQ)

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