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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) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

x^{2} + 6 x + 9 :

Minimum

(- 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) \geq 0

Graph

Popular Examples

inverse of f(x)=x^2+4x+5

domain of f(x)=sqrt(6-5x)

domain of 3(3x+6)+6

domain of (sqrt(x+9))/(sqrt(x+8))

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