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Popular >

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

Solution

range

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

Solution

f (x) \geq - 4

+1

Interval Notation

[- 4, \infty)

Solution steps

Vertex of

x^{2} - 2 x - 3 :

Minimum

(1, - 4)

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}) = (1, - 4)

f (x) \geq - 4

Popular Examples

parity x/(x^2-1)parity

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

domain of (4x+8)/(x^2+4x-32)domain

\frac{4 x + 8}{x ^{2} + 4 x - 32}

domain of sqrt(5x)+7x-2 domain

5 x + 7 x - 2

line m= 18/7 ,(-6,-3)line

m = \frac{18}{7}, (- 6, - 3)

symmetry (x-1)/(x+1)symmetry

\frac{x - 1}{x + 1}

Frequently Asked Questions (FAQ)

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