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Popular >

range of x^2+x+3

Solution

range

x^{2} + x + 3

Solution

f (x) \geq \frac{11}{4}

+1

Interval Notation

[\frac{11}{4}, \infty)

Solution steps

Vertex of

x^{2} + x + 3 :

Minimum

(- \frac{1}{2}, \frac{11}{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{11}{4})

f (x) \geq \frac{11}{4}

Popular Examples

line m= 5/8 ,(9,4)line

m = \frac{5}{8}, (9, 4)

domain of f(x)=sqrt(7-2x)+2 domain

f (x) = 7 - 2 x + 2

intercepts of (x^2+4x-5)/(x-1)intercepts

\frac{x ^{2} + 4 x - 5}{x - 1}

asymptotes of (x^2+4x-5)/(x^2+x-2)asymptotes

\frac{x ^{2} + 4 x - 5}{x ^{2} + x - 2}

inverse of f(x)=sqrt(x+7)-1 inverse

f (x) = x + 7 - 1

Frequently Asked Questions (FAQ)

What is the range of x^2+x+3 ?
The range of x^2+x+3 is f(x)>= 11/4