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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

slope ofintercept 2x-3y=12 slope intercept

2 x - 3 y = 12

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

parity f(x)=(3x+5)/(x-2)parity

f (x) = \frac{3 x + 5}{x - 2}

domain of (x/(x+1))/(x/(x+1)+1)domain

\frac{\frac{x}{x + 1}}{\frac{x}{x + 1} + 1}

slope of y=8x-5 slope

y = 8 x - 5

Frequently Asked Questions (FAQ)

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