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Popular >

range of f(x)=(x+1)^2-4

Solution

range

f (x) = (x + 1)^{2} - 4

Solution

f (x) \geq - 4

+1

Interval Notation

[- 4, \infty)

Solution steps

Vertex of

(x + 1)^{2} - 4 :

Minimum

(- 1, - 4)

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}) = (- 1, - 4)

f (x) \geq - 4

Popular Examples

inflection f(x)=x^3-4x^2-16x+9 inflection points

f (x) = x^{3} - 4 x^{2} - 16 x + 9

inverse of y=log_{5}(x)-9 inverse

y = lo g_{5} (x) - 9

line (4,11),(9,26)line

(4, 11), (9, 26)

domain of f(x)=(x+2)^{1/2}domain

f (x) = (x + 2)^{\frac{1}{2}}

slope of y=8 slope

y = 8

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x+1)^2-4 ?
The range of f(x)=(x+1)^2-4 is f(x)>=-4