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Popular >

range of 2x^2+4x+3

Solution

range

2 x^{2} + 4 x + 3

Solution

f (x) \geq 1

+1

Interval Notation

[1, \infty)

Solution steps

Vertex of

2 x^{2} + 4 x + 3 :

Minimum

(- 1, 1)

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, 1)

f (x) \geq 1

Popular Examples

inverse of f(x)=(x-3)^2+7 inverse

f (x) = (x - 3)^{2} + 7

domain of f(x)=((-x+1)/x+2)/((-x+1)/x-9)domain

f (x) = \frac{\frac{- x + 1}{x} + 2}{\frac{- x + 1}{x} - 9}

f (t) = t^{2}

monotone f(x)=(x+7)^3-2 monotone intervals

f (x) = (x + 7)^{3} - 2

inverse of f(x)=2x-3 inverse

f (x) = 2 x - 3

Frequently Asked Questions (FAQ)

What is the range of 2x^2+4x+3 ?
The range of 2x^2+4x+3 is f(x)>= 1