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Popular >

range of x^2-2x+1

Solution

range

x^{2} - 2 x + 1

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

x^{2} - 2 x + 1 :

Minimum

(1, 0)

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, 0)

f (x) \geq 0

Popular Examples

domain of f(x)=x^3+4x^2 domain

f (x) = x^{3} + 4 x^{2}

domain of f(x)=(x-3)/x domain

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

critical x/(sqrt(x^2+1))critical points

\frac{x}{x ^{2} + 1}

inverse of (3-3x)/(3x+4)inverse

\frac{3 - 3 x}{3 x + 4}

line m=-2/3 ,(-5,-3)line

m = - \frac{2}{3}, (- 5, - 3)

Frequently Asked Questions (FAQ)

What is the range of x^2-2x+1 ?
The range of x^2-2x+1 is f(x)>= 0