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Popular Functions >

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

Solution

range

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

Solution

f (x) \leq 8

+1

Interval Notation

(- \infty, 8]

Solution steps

Vertex of

- x^{2} + 6 x - 1 :

Maximum

(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) \leq 8

Graph

Popular Examples

extreme f(x)=(x^2+x+2)/(x-1)

e x t re m e f (x) = \frac{x ^{2} + x + 2}{x - 1}

inverse of f(x)=-x^2-4x-3

in v erse f (x) = - x^{2} - 4 x - 3

distance (0,0),(2,-3)

d i s t an ce (0, 0), (2, - 3)

inverse of log_{e}((2-x)/(x+3))

in v erse lo g_{e} (\frac{2 - x}{x + 3})

domain of f(x)=3-x

d o main f (x) = 3 - x

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