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Popular >

range of (x-3)^2-9

Solution

range

(x - 3)^{2} - 9

Solution

f (x) \geq - 9

+1

Interval Notation

[- 9, \infty)

Solution steps

Vertex of

(x - 3)^{2} - 9 :

Minimum

(3, - 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}) = (3, - 9)

f (x) \geq - 9

Popular Examples

intercepts of f(x)= 3/(x+6)intercepts

f (x) = \frac{3}{x + 6}

inverse of f(x)=(1-4x)/(3x+7)inverse

f (x) = \frac{1 - 4 x}{3 x + 7}

domain of f(x)=sqrt(x+6)-(sqrt(7-x))/x domain

f (x) = x + 6 - \frac{7 - x}{x}

inverse of f(x)=log_{4}(x-1)inverse

f (x) = lo g_{4} (x - 1)

inverse of x^3-27 inverse

x^{3} - 27

Frequently Asked Questions (FAQ)

What is the range of (x-3)^2-9 ?
The range of (x-3)^2-9 is f(x)>=-9