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Popular Functions >

range of f(x)=-x^2+6x-9

Solution

range

f (x) = - x^{2} + 6 x - 9

Solution

f (x) \leq 0

+1

Interval Notation

(- \infty, 0]

Solution steps

Vertex of

- x^{2} + 6 x - 9 :

Maximum

(3, 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}) = (3, 0)

f (x) \leq 0

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the range of f(x)=-x^2+6x-9 ?
The range of f(x)=-x^2+6x-9 is f(x)<= 0