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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

critical (x^4)/4-x^2+1 critical points

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

3 x + 5

critical x+1/x critical points

x + \frac{1}{x}

symmetry x^2+y-9=0 symmetry

x^{2} + y - 9 = 0

domain of 1/(5+3x)domain

\frac{1}{5 + 3 x}

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