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Popular >

range of f(x)=16-(x-2)^2

Solution

range

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

Solution

f (x) \leq 16

+1

Interval Notation

(- \infty, 16]

Solution steps

Vertex of

16 - (x - 2)^{2} :

Maximum

(2, 16)

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, 16)

f (x) \leq 16

Popular Examples

midpoint (4,-2),(0,2)midpoint

(4, - 2), (0, 2)

distance (7,-4),(-2,-7)distance

(7, - 4), (- 2, - 7)

inflection f(x)=x^3-7x^2-24x+7 inflection points

f (x) = x^{3} - 7 x^{2} - 24 x + 7

domain of G domain

G

midpoint (9,-8),(2,-5)midpoint

(9, - 8), (2, - 5)

Frequently Asked Questions (FAQ)

What is the range of f(x)=16-(x-2)^2 ?
The range of f(x)=16-(x-2)^2 is f(x)<= 16