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Popular >

range of f(x)=(x-3)^2

Solution

range

f (x) = (x - 3)^{2}

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

(x - 3)^{2} :

Minimum

(3, 0)

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, 0)

f (x) \geq 0

Popular Examples

inverse of f(x)=(x+9)/(x+5)inverse

f (x) = \frac{x + 9}{x + 5}

inflection x^3-6x^2-63x inflection points

x^{3} - 6 x^{2} - 63 x

inverse of 4x inverse

4 x

distance (-3,-1),(-4,-0)distance

(- 3, - 1), (- 4, - 0)

vertices y=x^2+4x-5 vertices

y = x^{2} + 4 x - 5

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x-3)^2 ?
The range of f(x)=(x-3)^2 is f(x)>= 0