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Popular Functions >

range of f(x)=(x+2)^2-5

Solution

range

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

Solution

f (x) \geq - 5

+1

Interval Notation

[- 5, \infty)

Solution steps

Vertex of

(x + 2)^{2} - 5 :

Minimum

(- 2, - 5)

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}) = (- 2, - 5)

f (x) \geq - 5

Graph

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Frequently Asked Questions (FAQ)

What is the range of f(x)=(x+2)^2-5 ?
The range of f(x)=(x+2)^2-5 is f(x)>=-5