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Popular >

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

Solution

range

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

Solution

f (x) \geq - 3

+1

Interval Notation

[- 3, \infty)

Solution steps

Vertex of

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

Minimum

(- 1, - 3)

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}) = (- 1, - 3)

f (x) \geq - 3

Popular Examples

midpoint (2,-4),(-4,0)midpoint

(2, - 4), (- 4, 0)

intercepts of (x+1)/(x^2-x-2)intercepts

\frac{x + 1}{x ^{2} - x - 2}

inverse of f(x)=sqrt(4-25/9 (x+2)^2)inverse

f (x) = 4 - \frac{25}{9} (x + 2)^{2}

inverse of f(n)=(-16+n)/4 inverse

f (n) = \frac{- 16 + n}{4}

domain of f(x)=sqrt(x^2-4x-12)domain

f (x) = x^{2} - 4 x - 12

Frequently Asked Questions (FAQ)

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