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Popular >

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

Solution

range

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

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

x^{2} - 2 x :

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 = 1,

Vertex

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

f (x) \geq - 1

Popular Examples

midpoint (0,-4),(10,-3)midpoint

(0, - 4), (10, - 3)

inverse of f(x)=(x-8)^{1/2}inverse

f (x) = (x - 8)^{\frac{1}{2}}

inverse of f(x)=3(x-4)+10 inverse

f (x) = 3 (x - 4) + 10

inverse of f(x)= 1/3 x^3-6 inverse

f (x) = \frac{1}{3} x^{3} - 6

domain of-(21)/((5+t)^2)domain

- \frac{21}{( 5 + t ) ^{2}}

Frequently Asked Questions (FAQ)

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