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Popular Functions >

range of f(x)=(x+3)^2-1

Solution

range

f (x) = (x + 3)^{2} - 1

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

(x + 3)^{2} - 1 :

Minimum

(- 3, - 1)

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, - 1)

f (x) \geq - 1

Graph

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Frequently Asked Questions (FAQ)

What is the range of f(x)=(x+3)^2-1 ?
The range of f(x)=(x+3)^2-1 is f(x)>=-1