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Popular >

range of x^2-4x+4

Solution

range

x^{2} - 4 x + 4

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

x^{2} - 4 x + 4 :

Minimum

(2, 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}) = (2, 0)

f (x) \geq 0

Popular Examples

critical f(x)=(x+4)(x-1)^2 critical points

f (x) = (x + 4) (x - 1)^{2}

range of f(x)=sqrt(x+5)range

f (x) = x + 5

inflection f(x)=xsqrt(9-x)inflection points

f (x) = x 9 - x

asymptotes of (x^2+25)/x asymptotes

\frac{x ^{2} + 25}{x}

domain of y=-3 domain

y = - 3

Frequently Asked Questions (FAQ)

What is the range of x^2-4x+4 ?
The range of x^2-4x+4 is f(x)>= 0