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Popular >

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

Popular Examples

inverse of f(x)=x^2+5,x>= 0 inverse

f (x) = x^{2} + 5, x \geq 0

range of f(x)=5csc(1/3 x)-1 range

f (x) = 5 csc (\frac{1}{3} x) - 1

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

(1, 2), (5, 6)

range of 2/(x-2)-8 range

\frac{2}{x - 2} - 8

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

\frac{3}{x + 2} - x - 3

Frequently Asked Questions (FAQ)

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