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Popular >

range of f(x)=x^2-2x+1

Solution

range

f (x) = 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

perpendicular y=-x+4 perpendicular

y = - x + 4

inverse of f(x)=(x-14)^2 inverse

f (x) = (x - 14)^{2}

perpendicular 5x-2y=-3 perpendicular

5 x - 2 y = - 3

midpoint (2.5,4.6),(9.5,1.6)midpoint

(2.5, 4.6), (9.5, 1.6)

slope ofintercept x-y=-8 slope intercept

x - y = - 8

Frequently Asked Questions (FAQ)

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