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Popular >

range of x^2+4x+3

Solution

range

x^{2} + 4 x + 3

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

x^{2} + 4 x + 3 :

Minimum

(- 2, - 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 = 1,

Vertex

(x_{v}, y_{v}) = (- 2, - 1)

f (x) \geq - 1

Popular Examples

inverse of f(x)=3+sqrt(6+9x)inverse

f (x) = 3 + 6 + 9 x

inflection (x^2-16)/(x+4)inflection points

\frac{x ^{2} - 16}{x + 4}

domain of f(x)=(-1)/(x^2)domain

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

parity f(x)= 3/(x^4+7x+1)parity

f (x) = \frac{3}{x ^{4} + 7 x + 1}

inverse of f(x)=(10x)/(x^2+49)inverse

f (x) = \frac{10 x}{x ^{2} + 49}

Frequently Asked Questions (FAQ)

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