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Popular >

range of f(x)=(x-4)^2+5

Solution

range

f (x) = (x - 4)^{2} + 5

Solution

f (x) \geq 5

+1

Interval Notation

[5, \infty)

Solution steps

Vertex of

(x - 4)^{2} + 5 :

Minimum

(4, 5)

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}) = (4, 5)

f (x) \geq 5

Popular Examples

parity 3x parity

3 x

perpendicular y=-3/4 x+1,(9,12)perpendicular

y = - \frac{3}{4} x + 1, (9, 12)

inverse of f(x)=x^2+8x-6 inverse

f (x) = x^{2} + 8 x - 6

domain of f(x)=-x^2+2x+1 domain

f (x) = - x^{2} + 2 x + 1

asymptotes of f(x)=xe^{-4x}asymptotes

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

Frequently Asked Questions (FAQ)

What is the range of f(x)=(x-4)^2+5 ?
The range of f(x)=(x-4)^2+5 is f(x)>= 5