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Popular >

range of (x-1)^2+4

Solution

range

(x - 1)^{2} + 4

Solution

f (x) \geq 4

+1

Interval Notation

[4, \infty)

Solution steps

Vertex of

(x - 1)^{2} + 4 :

Minimum

(1, 4)

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}) = (1, 4)

f (x) \geq 4

Popular Examples

range of x/(1-x)range

\frac{x}{1 - x}

inflection e^{-1.5x^2}inflection points

e^{- 1.5 x^{2}}

inverse of sqrt(3-e^{2x)}inverse

3 - e^{2 x}

asymptotes of f(x)=((x+9))/(x^2+4x)asymptotes

f (x) = \frac{( x + 9 )}{x ^{2} + 4 x}

intercepts of x^5-4x^3 intercepts

x^{5} - 4 x^{3}

Frequently Asked Questions (FAQ)

What is the range of (x-1)^2+4 ?
The range of (x-1)^2+4 is f(x)>= 4