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Popular >

range of f(x)=x^2-4x+3

Solution

range

f (x) = 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

domain of f(x)=sqrt(9+4x)domain

f (x) = 9 + 4 x

asymptotes of f(x)=x*e^{1/x}asymptotes

f (x) = x \cdot e^{\frac{1}{x}}

domain of f(x)=(x+5)/4 domain

f (x) = \frac{x + 5}{4}

slope ofintercept y+5=-1/5 (x+1)slope intercept

y + 5 = - \frac{1}{5} (x + 1)

domain of (x-1)/(x+3)domain

\frac{x - 1}{x + 3}

Frequently Asked Questions (FAQ)

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