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Popular >

range of (x+1)^2

Solution

range

(x + 1)^{2}

Solution

f (x) \geq 0

+1

Interval Notation

[0, \infty)

Solution steps

Vertex of

(x + 1)^{2} :

Minimum

(- 1, 0)

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 = 1,

Vertex

(x_{v}, y_{v}) = (- 1, 0)

f (x) \geq 0

Popular Examples

inverse of f(x)=(sqrt(3x+2))/4 inverse

f (x) = \frac{3 x + 2}{4}

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

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

critical f(x)=-32t+30 critical points

f (x) = - 32 t + 30

parity f(x)=sqrt(2x^2+1)parity

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

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

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

Frequently Asked Questions (FAQ)

What is the range of (x+1)^2 ?
The range of (x+1)^2 is f(x)>= 0