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Popular >

range of 2(x-1)^2+3

Solution

range

2 (x - 1)^{2} + 3

Solution

f (x) \geq 3

+1

Interval Notation

[3, \infty)

Solution steps

Vertex of

2 (x - 1)^{2} + 3 :

Minimum

(1, 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 = 2,

Vertex

(x_{v}, y_{v}) = (1, 3)

f (x) \geq 3

Popular Examples

simplify (3.1)(7)simplify

(3.1) (7)

inverse of f(x)= 1/2 x-2 inverse

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

domain of 7+(4+x)^{1/2}domain

7 + (4 + x)^{\frac{1}{2}}

critical y=x^2e^x critical points

y = x^{2} e^{x}

asymptotes of f(x)=(x^2+25)/(x^2-4)asymptotes

f (x) = \frac{x ^{2} + 25}{x ^{2} - 4}

Frequently Asked Questions (FAQ)

What is the range of 2(x-1)^2+3 ?
The range of 2(x-1)^2+3 is f(x)>= 3