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Popular Functions >

range of f(x)=-1/2 (x+6)^2+8

Solution

range

f (x) = - \frac{1}{2} (x + 6)^{2} + 8

Solution

f (x) \leq 8

+1

Interval Notation

(- \infty, 8]

Solution steps

Vertex of

- \frac{1}{2} (x + 6)^{2} + 8 :

Maximum

(- 6, 8)

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}{2},

Vertex

(x_{v}, y_{v}) = (- 6, 8)

f (x) \leq 8

Graph

Popular Examples

extreme f(x)=x^3+10

e x t re m e f (x) = x^{3} + 10

y = - 3 x

extreme f(x)=-x^3+12x-16

e x t re m e f (x) = - x^{3} + 12 x - 16

in v erse - x + 3

periodicity of f(x)= 4/3-2cos(2+1/3 x)

p er i o d i c i t y f (x) = \frac{4}{3} - 2 cos (2 + \frac{1}{3} x)

Frequently Asked Questions (FAQ)

What is the range of f(x)=-1/2 (x+6)^2+8 ?
The range of f(x)=-1/2 (x+6)^2+8 is f(x)<= 8