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Popular Functions >

range of x^2-4x+1

Solution

range

x^{2} - 4 x + 1

Solution

f (x) \geq - 3

+1

Interval Notation

[- 3, \infty)

Solution steps

Vertex of

x^{2} - 4 x + 1 :

Minimum

(2, - 3)

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, - 3)

f (x) \geq - 3

Graph

Popular Examples

domain of f(x)= 2/(x+7)

perpendicular-3/4

asymptotes of y=2+log_{3}(x)

domain of f(x)=(x-3)^2+1

extreme f(x)=x^3-6x^2+9

Frequently Asked Questions (FAQ)

What is the range of x^2-4x+1 ?
The range of x^2-4x+1 is f(x)>=-3