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Popular >

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}

Popular Examples

inverse of f(x)=-x-9 inverse

f (x) = - x - 9

distance (4,7),(1,6)distance

(4, 7), (1, 6)

inverse of-5x+4 inverse

- 5 x + 4

extreme f(x)=3-2x-x^2 extreme points

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

slope of y=3x+8 slope

y = 3 x + 8

Frequently Asked Questions (FAQ)

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