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Popular Functions >

range of x^2+x+1

Solution

range

x^{2} + x + 1

Solution

f (x) \geq \frac{3}{4}

+1

Interval Notation

[\frac{3}{4}, \infty)

Solution steps

Vertex of

x^{2} + x + 1 :

Minimum

(- \frac{1}{2}, \frac{3}{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{3}{4})

f (x) \geq \frac{3}{4}

Graph

Popular Examples

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domain of y=sqrt(x-1)

asymptotes of f(x)= 3/(x-5)

Frequently Asked Questions (FAQ)

What is the range of x^2+x+1 ?
The range of x^2+x+1 is f(x)>= 3/4