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Popular >

range of f(x)=x^2-6x+1

Solution

range

f (x) = x^{2} - 6 x + 1

Solution

f (x) \geq - 8

+1

Interval Notation

[- 8, \infty)

Solution steps

Vertex of

x^{2} - 6 x + 1 :

Minimum

(3, - 8)

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}) = (3, - 8)

f (x) \geq - 8

Popular Examples

critical f(x)=x^2-x-20 critical points

f (x) = x^{2} - x - 20

critical f(x)=cos(4x)critical points

f (x) = cos (4 x)

parallel 9x-y=-18,(0,0)parallel

9 x - y = - 18, (0, 0)

domain of f(x)=-sqrt(x-1)-2 domain

f (x) = - x - 1 - 2

asymptotes of f(x)=(x^2-x-2)/(x^2-5x+6)asymptotes

f (x) = \frac{x ^{2} - x - 2}{x ^{2} - 5 x + 6}

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-6x+1 ?
The range of f(x)=x^2-6x+1 is f(x)>=-8