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Popular >

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

Solution

range

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

Solution

f (x) \leq - 5

+1

Interval Notation

(- \infty, - 5]

Solution steps

Vertex of

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

Maximum

(- 3, - 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 = - 2,

Vertex

(x_{v}, y_{v}) = (- 3, - 5)

f (x) \leq - 5

Popular Examples

domain of f(x)=sqrt(2x-14)domain

f (x) = 2 x - 14

critical x^4-8x^3+10 critical points

x^{4} - 8 x^{3} + 10

slope ofintercept 8x+2y=-10 slope intercept

8 x + 2 y = - 10

asymptotes of f(x)=(-3)/(2x-1)asymptotes

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

inverse of 2x^2+5 inverse

2 x^{2} + 5

Frequently Asked Questions (FAQ)

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