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Popular >

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

Solution

range

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

Solution

f (x) \geq - 1

+1

Interval Notation

[- 1, \infty)

Solution steps

Vertex of

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

Minimum

(- 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) \geq - 1

Popular Examples

inverse of f(x)=9x^2,x>= 0 inverse

f (x) = 9 x^{2}, x \geq 0

inverse of f(x)=x^7+3 inverse

f (x) = x^{7} + 3

monotone f(x)=(x^2-3)/(x-2)monotone intervals

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

intercepts of f(x)=-4(x-2)^2-3 intercepts

f (x) = - 4 (x - 2)^{2} - 3

inverse of f(x)=2x^3+1 inverse

f (x) = 2 x^{3} + 1

Frequently Asked Questions (FAQ)

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