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Popular Functions >

range of (x-2)^2+1

Solution

range

(x - 2)^{2} + 1

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

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

Minimum

(2, 1)

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, 1)

f (x) \geq 1

Graph

Popular Examples

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line (1,2),(5,6)

parity 3/(x+2)-sqrt(x-3)

range of f(x)=(4x^2+4x-1)/(2x^3+8x^2)

Frequently Asked Questions (FAQ)

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