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Popular >

range of (x-2)^2+3

Solution

range

(x - 2)^{2} + 3

Solution

f (x) \geq 3

+1

Interval Notation

[3, \infty)

Solution steps

Vertex of

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

Minimum

(2, 3)

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, 3)

f (x) \geq 3

Popular Examples

asymptotes of x^3-4x^2+4x-3 asymptotes

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

intercepts of f(x)= 2/3 x-4 intercepts

f (x) = \frac{2}{3} x - 4

slope ofintercept 3x+15y=45 slope intercept

3 x + 15 y = 45

domain of |x^2-1|domain

x^{2} - 1

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

f (x) = - x + 5

Frequently Asked Questions (FAQ)

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