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Popular >

range of (x-3)^2

Solution

range

(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

domain of f(x)= 9/(\frac{x){9/x+9}}domain

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

inverse of h(x)=5^x inverse

h (x) = 5^{x}

domain of f(x)=(x-3)/(x^2+9x-22)domain

f (x) = \frac{x - 3}{x ^{2} + 9 x - 22}

y = 3

range of (sqrt(x-5))/(x-10)range

\frac{x - 5}{x - 10}

Frequently Asked Questions (FAQ)

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