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Popular >

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

Solution

range

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

Solution

f (x) \geq 3

+1

Interval Notation

[3, \infty)

Solution steps

Vertex of

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

Minimum

(2, 3)

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}) = (2, 3)

f (x) \geq 3

Popular Examples

line (-2,-6),(4,6)line

(- 2, - 6), (4, 6)

line y=8x-7 line

y = 8 x - 7

domain of (-6x+23)/(7x-16)domain

\frac{- 6 x + 23}{7 x - 16}

domain of h(x)=(sqrt(2))/(sqrt(x^2-4))domain

h (x) = \frac{2}{x ^{2} - 4}

inflection f(x)=(x^2)/(8x^2+2)inflection points

f (x) = \frac{x ^{2}}{8 x ^{2} + 2}

Frequently Asked Questions (FAQ)

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