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Popular Functions >

range of x^2-x

Solution

range

x^{2} - x

Solution

f (x) \geq - \frac{1}{4}

+1

Interval Notation

[- \frac{1}{4}, \infty)

Solution steps

Vertex of

x^{2} - x :

Minimum

(\frac{1}{2}, - \frac{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}) = (\frac{1}{2}, - \frac{1}{4})

f (x) \geq - \frac{1}{4}

Graph

Popular Examples

inverse of f(x)=-x-9

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

extreme f(x)= 5/(x^2-49)

inverse of f(x)=((x+19))/((x-17))

domain of f(x)=-1/(2x^{3/2)}

Frequently Asked Questions (FAQ)

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