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Popular >

range of (x+3)^2-1

Solution

range

(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

Popular Examples

inflection-1/2 x^4+48x^2 inflection points

- \frac{1}{2} x^{4} + 48 x^{2}

perpendicular y= 1/4 x+9,\at (2-2)perpendicular

y = \frac{1}{4} x + 9, at (2 - 2)

asymptotes of f(x)=((-4x^2-2x+1))/(2x+3)asymptotes

f (x) = \frac{( - 4 x ^{2} - 2 x + 1 )}{2 x + 3}

domain of f(x)= 1/(2x-8)domain

f (x) = \frac{1}{2 x - 8}

asymptotes of f(x)=(-4x^2-3x+8)/(x+1)asymptotes

f (x) = \frac{- 4 x ^{2} - 3 x + 8}{x + 1}

Frequently Asked Questions (FAQ)

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