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Popular >

range of f(x)= 1/3 (x-2)^2+5

Solution

range

f (x) = \frac{1}{3} (x - 2)^{2} + 5

Solution

f (x) \geq 5

+1

Interval Notation

[5, \infty)

Solution steps

Vertex of

\frac{1}{3} (x - 2)^{2} + 5 :

Minimum

(2, 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 = \frac{1}{3},

Vertex

(x_{v}, y_{v}) = (2, 5)

f (x) \geq 5

Popular Examples

intercepts of f(x)=(4x)/(2x-6)intercepts

f (x) = \frac{4 x}{2 x - 6}

critical (x^3(x-5)^2)/(54)critical points

\frac{x ^{3} ( x - 5 ) ^{2}}{54}

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

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

intercepts of f(x)=(x^2-2x-8)/(x-6)intercepts

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

midpoint (-5,-4),(9,2)midpoint

(- 5, - 4), (9, 2)

Frequently Asked Questions (FAQ)

What is the range of f(x)= 1/3 (x-2)^2+5 ?
The range of f(x)= 1/3 (x-2)^2+5 is f(x)>= 5