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Popular >

range of x^2-3x+3

Solution

range

x^{2} - 3 x + 3

Solution

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

+1

Interval Notation

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

Solution steps

Vertex of

x^{2} - 3 x + 3 :

Minimum

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

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

Popular Examples

inverse of x^3+7 inverse

x^{3} + 7

asymptotes of f(x)=(-3x)/(2x+7)asymptotes

f (x) = \frac{- 3 x}{2 x + 7}

critical x^2sqrt(5+x)critical points

x^{2} 5 + x

parity tan(2x)cos(x)parity

tan (2 x) cos (x)

domain of 1/(-10(\frac{1){-5x-6}+3)}domain

\frac{1}{- 10 ( \frac{1}{- 5 x - 6} + 3 )}

Frequently Asked Questions (FAQ)

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