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Popular >

range of x^2-2x-3

Solution

range

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

amplitude of 1/9 sin(7x+pi/2)amplitude

\frac{1}{9} sin (7 x + \frac{π}{2})

inverse of (2x+3)/(5x+4)inverse

\frac{2 x + 3}{5 x + 4}

f(x)=x^2-3x,g(x)=sqrt(x-1),g(x)\circ f(x)

f (x) = x^{2} - 3 x, g (x) = x - 1, g (x) \circ f (x)

intercepts of y=x-4 intercepts

y = x - 4

asymptotes of f(x)=(x^2+x-9)/(x-2)asymptotes

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

Frequently Asked Questions (FAQ)

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