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Popular >

range of-2(x+3)^2-1

Solution

range

- 2 (x + 3)^{2} - 1

Solution

f (x) \leq - 1

+1

Interval Notation

(- \infty, - 1]

Solution steps

Vertex of

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

Maximum

(- 3, - 1)

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, - 1)

f (x) \leq - 1

Popular Examples

y = 2 x - 7

inverse of ln(2)inverse

ln (2)

asymptotes of e^x(x^3-4x^2+7x-6)asymptotes

e^{x} (x^{3} - 4 x^{2} + 7 x - 6)

critical x^2+4x-4 critical points

x^{2} + 4 x - 4

inverse of (x-1)/(x+3)inverse

\frac{x - 1}{x + 3}

Frequently Asked Questions (FAQ)

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