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Popular >

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

Solution

range

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

Solution

f (x) \geq - 2

+1

Interval Notation

[- 2, \infty)

Solution steps

Vertex of

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

Minimum

(- 3, - 2)

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, - 2)

f (x) \geq - 2

Popular Examples

domain of f(x)=2x^2+8x domain

f (x) = 2 x^{2} + 8 x

domain of g(x)=sqrt(4-x)+sqrt(x^2-1)domain

g (x) = 4 - x + x^{2} - 1

parity f(x)=|x+2|+|x-2|parity

f (x) = ∣ x + 2 ∣ + ∣ x - 2 ∣

domain of y=3x+2 domain

y = 3 x + 2

critical f(x)=x^3-3x^2+3x-2 critical points

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

Frequently Asked Questions (FAQ)

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