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Popular >

range of f(x)=x^2-4x+7

Solution

range

f (x) = x^{2} - 4 x + 7

Solution

f (x) \geq 3

+1

Interval Notation

[3, \infty)

Solution steps

Vertex of

x^{2} - 4 x + 7 :

Minimum

(2, 3)

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, 3)

f (x) \geq 3

Popular Examples

domain of y=sqrt(2x-5)domain

y = 2 x - 5

critical e^{-x^2}critical points

e^{- x^{2}}

intercepts of f(x)=2x^2-12x+16 intercepts

f (x) = 2 x^{2} - 12 x + 16

midpoint (-2,3),(-2,-3)midpoint

(- 2, 3), (- 2, - 3)

intercepts of f(x)=x^3-x^4 intercepts

f (x) = x^{3} - x^{4}

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-4x+7 ?
The range of f(x)=x^2-4x+7 is f(x)>= 3