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Popular >

range of f(x)=x^2-x+3

Solution

range

f (x) = 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

inverse of f(x)=(7-x)^2 inverse

f (x) = (7 - x)^{2}

intercepts of f(x)=(6x)/(x^2-4)intercepts

f (x) = \frac{6 x}{x ^{2} - 4}

critical f(x)=-(2/(x^2+1))critical points

f (x) = - (\frac{2}{x ^{2} + 1})

domain of f(x)= 1/(sqrt(1+2x))domain

f (x) = \frac{1}{1 + 2 x}

midpoint (0,1),(1,-1)midpoint

(0, 1), (1, - 1)

Frequently Asked Questions (FAQ)

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