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Popular >

range of f(x)=x^2+4x+3

Solution

range

f (x) = 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

domain of 8/3 x-3 domain

\frac{8}{3} x - 3

domain of f(x)=(x+5)/(x^2-1)domain

f (x) = \frac{x + 5}{x ^{2} - 1}

domain of f(x)=-2/5 (x-5)^2+10 domain

f (x) = - \frac{2}{5} (x - 5)^{2} + 10

domain of (7x-1)/(4x^2-27x-81)domain

\frac{7 x - 1}{4 x ^{2} - 27 x - 81}

domain of 1/6 x^2-1 domain

\frac{1}{6} x^{2} - 1

Frequently Asked Questions (FAQ)

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