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Popular >

range of x^2-4x+3

Solution

range

x^{2} - 4 x + 3

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

x^{2} - 4 x + 3 :

Minimum

(2, - 1)

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}) = (2, - 1)

f (x) \geq - 1

Popular Examples

parity f(x)=x^2+2 parity

f (x) = x^{2} + 2

domain of ln(x)+6 domain

ln (x) + 6

extreme-x^4+4x^3+2 extreme points

- x^{4} + 4 x^{3} + 2

range of 3/5 sqrt(x-3)-3 range

\frac{3}{5} x - 3 - 3

inflection f(x)=-1/3 x^3+7x^2 inflection points

f (x) = - \frac{1}{3} x^{3} + 7 x^{2}

Frequently Asked Questions (FAQ)

What is the range of x^2-4x+3 ?
The range of x^2-4x+3 is f(x)>=-1