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Popular >

range of (x-5)^2-9

Solution

range

(x - 5)^{2} - 9

Solution

f (x) \geq - 9

+1

Interval Notation

[- 9, \infty)

Solution steps

Vertex of

(x - 5)^{2} - 9 :

Minimum

(5, - 9)

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}) = (5, - 9)

f (x) \geq - 9

Popular Examples

inflection e^{-0.5x^2}inflection points

e^{- 0.5 x^{2}}

domain of (4x+16)/x domain

\frac{4 x + 16}{x}

parity f(x)= x/(1-x^2)parity

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

domain of (sqrt(x-2))/(x-10)domain

\frac{x - 2}{x - 10}

asymptotes of f(x)=(3x-15)/(-x^2+5x)asymptotes

f (x) = \frac{3 x - 15}{- x ^{2} + 5 x}

Frequently Asked Questions (FAQ)

What is the range of (x-5)^2-9 ?
The range of (x-5)^2-9 is f(x)>=-9