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Popular >

range of 2x(x-1)

Solution

range

2 x (x - 1)

Solution

f (x) \geq - \frac{1}{2}

+1

Interval Notation

[- \frac{1}{2}, \infty)

Solution steps

Vertex of

2 x (x - 1) :

Minimum

(\frac{1}{2}, - \frac{1}{2})

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 = 2,

Vertex

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

f (x) \geq - \frac{1}{2}

Popular Examples

domain of f(x)=-16t^2+64t+720 domain

f (x) = - 16 t^{2} + 64 t + 720

parallel y=4x+6 parallel

y = 4 x + 6

range of (2x^2-3)/(x^2)range

\frac{2 x ^{2} - 3}{x ^{2}}

range of sqrt(-x-3)range

- x - 3

periodicity of y=5sin(-2x-pi/2)periodicity

y = 5 sin (- 2 x - \frac{π}{2})

Frequently Asked Questions (FAQ)

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