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Popular >

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

Solution

range

f (x) = 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

domain of y=tan(2x-pi/3)domain

y = tan (2 x - \frac{π}{3})

intercepts of f(x)=x^2-x-8 intercepts

f (x) = x^{2} - x - 8

extreme 7-6cos(θ)extreme points

7 - 6 cos (θ)

distance (-5,2),(-2,6)distance

(- 5, 2), (- 2, 6)

inverse of f(x)= 1/3 inverse

f (x) = \frac{1}{3}

Frequently Asked Questions (FAQ)

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